ACTIVITY: Graphing a Linear Equation. 2 x x + 1?

Size: px
Start display at page:

Download "ACTIVITY: Graphing a Linear Equation. 2 x x + 1?"

Transcription

1 . Graphing Linear Equations How can ou draw its graph? How can ou recognize a linear equation? ACTIVITY: Graphing a Linear Equation Work with a partner. a. Use the equation = + to complete the table. (Choose an two -values and find the -values.) b. Write the two ordered pairs given b the table. These are called solution points of the equation. c. PRECISION Plot the two solution points. Draw a line eactl through the two points. d. Find a different point on the line. Check that this point is a solution point of the equation = +. e. LOGIC Do ou think it is true that an point on the line is a solution = Solution Points 6 5 O point of the equation = +? Eplain. f. Choose five additional -values for the table. (Choose positive and negative -values.) Plot the five corresponding solution points. Does each point lie on the line? COMMON CORE Graphing Equations In this lesson, ou will understand that lines represent solutions of linear equations. graph linear equations. Learning Standards A.CED. A.REI.0 = + Solution Points g. LOGIC Do ou think it is true that an solution point of the equation = + is a point on the line? Eplain. h. THE MEANING OF A WORD Wh is = a + b called a linear equation? Chapter Graphing and Writing Linear Equations

2 ACTIVITY: Using a Graphing Calculator Math Practice Recognize Usefulness of Tools What are some advantages and disadvantages of using a graphing calculator to graph a linear equation? Use a graphing calculator to graph = + 5. a. Enter the equation = + 5 into our calculator. b. Check the settings of the viewing window. The boundaries of the graph are set b the minimum and maimum - and -values. The number of units between the tick marks are set b the - and -scales. This is the standard viewing window. c. Graph = + 5 on our calculator d. Change the settings of the viewing window to match those shown. 5 8 Compare the two graphs. 6. IN YOUR OWN WORDS How can ou recognize a linear equation? How can ou draw its graph? Write an equation that is linear. Write an equation that is not linear.. Use a graphing calculator to graph = 5 in the standard viewing window. a. Can ou tell where the line crosses the -ais? Can ou tell where the line crosses the -ais? b. How can ou adjust the viewing window so that ou can determine where the line crosses the - and -aes? 5. CHOOSE TOOLS You want to graph =.5.8. Would ou graph it b hand or using a graphing calculator? Wh? Use what ou learned about graphing linear equations to complete Eercises and on page 6. Section. Graphing Linear Equations

3 . Lesson Lesson Tutorials Ke Vocabular linear equation, p. solution of a linear equation, p. Remember An ordered pair (, ) is used to locate a point in a coordinate plane. Linear Equations A linear equation is an equation whose graph is a line. The points on the line are solutions of the equation. You can use a graph to show the solutions of a linear equation. The graph below is for the equation = +. (, ) 0 (, 0) 0 (0, ) (, ) (, 0) = + (0, ) (, ) EXAMPLE Graphing a Linear Equation Graph = +. Step : Make a table of values. Check = + (, ) = ( ) + (, ) 0 = (0) + (0, ) = () + (, ) (, ) = + (0, ) Step : Plot the ordered pairs. Step : Draw a line through the points. (, ) Graphing Horizontal and Vertical Lines The graph of = b is a horizontal line passing through (0, b). The graph of = a is a vertical line passing through (a, 0). b (0, b) O a (a, 0) O Chapter Graphing and Writing Linear Equations

4 EXAMPLE Graphing a Horizontal Line and a Vertical Line a. Graph =. b. Graph =. The graph of = is a horizontal line passing through (0, ). Draw a horizontal line through this point. The graph of = is a vertical line passing through (, 0). Draw a vertical line through this point. O (0, ) (, 0) O Eercises 5 6 Graph the linear equation. Use a graphing calculator to check our graph, if possible.. =. = +. =. =.5 EXAMPLE Real-Life Application The wind speed (in miles per hour) of a tropical storm is = + 66, where is the number of hours after the storm enters the Gulf of Meico. a. Graph the equation. b. When does the storm become a hurricane? a. Make a table of values. = + 66 (, ) 0 = (0) (0, 66) 76 = + 66 = () (, 68) 7 A tropical storm becomes a hurricane when wind speeds are at least 7 miles per hour. = () (, 70) = () (, 7) 68 6 Plot the ordered pairs and draw a line through the points b. From the graph, ou can see that = 7 when =. So, the storm becomes a hurricane hours after it enters the Gulf of Meico. 5. WHAT IF? In Eample, the wind speed of the storm is = When does the storm become a hurricane? Section. Graphing Linear Equations 5

5 . Eercises Help with Homework. VOCABULARY What tpe of graph represents the solutions of the equation = +?. WHICH ONE DOESN T BELONG? Which equation does not belong with the other three? Eplain our reasoning. = = = = 9+(-6)= +(-)= +(-9)= 9+(-)= PRECISION Cop and complete the table. Plot the two solution points and draw a line eactl through the two points. Find a different solution point on the line... = = + Graph the linear equation. Use a graphing calculator to check our graph, if possible. 5. = 5 6. = 7. = 5 8. = 6 9. = 0. = 7. = +. =. =. = = = 7. ERROR ANALYSIS Describe and correct the error in graphing the equation. 8. MESSAGING You sign up for an unlimited tet messaging plan for our cell phone. The equation = 0 represents the cost (in dollars) for sending tet messages. Graph the equation. What does the graph tell ou? O = (, 0) 9. MAIL The equation = + represents the cost (in dollars) of mailing a package that weighs pounds. a. Graph the equation. b. Use the graph to estimate how much it costs to mail the package. c. Use the equation to find eactl how much it costs to mail the package. 6 Chapter Graphing and Writing Linear Equations

6 Solve for. Then graph the equation. Use a graphing calculator to check our graph. 0. =. 5 + =. + = =.5. SAVINGS You have $00 in our savings account and plan to deposit $.50 each month. a. Write and graph a linear equation that represents the balance in our account. b. How man months will it take ou to save enough mone to bu 0 acres of land on Mars? Video time: min. 0 sec. 5. CAMERA One second of video on our digital camera uses the same amount of memor as two pictures. Your camera can store 50 pictures. a. Write and graph a linear equation that represents the number of pictures our camera can store if ou take seconds of video. b. How man pictures can our camera store after ou take the video shown? 6. PROBLEM SOLVING Along the U.S. Atlantic Coast, the sea level is rising about millimeters per ear. How man millimeters has sea level risen since ou were born? How do ou know? Use a linear equation and a graph to justif our answer. 7. The sum S of the measures of the angles of a polgon is S = (n ) 80, where n is the number of sides of the polgon. a. Plot four points (n, S ) that satisf the equation. Do the points lie on a line? Eplain our reasoning. b. Does the value n =.5 make sense in the contet of the problem? Eplain our reasoning. Write the ordered pair corresponding to the point. (Skills Review Handbook) B 6 8. Point A 9. Point B A 0. Point C. Point D. MULTIPLE CHOICE A debate team has 5 female members. The ratio of females to males is :. How man males are on the debate team? (Skills Review Handbook) 6 O A 6 B 0 C D 5 D C Section. Graphing Linear Equations 7

ACTIVITY: Graphing a Linear Equation. 2 x x + 1?

ACTIVITY: Graphing a Linear Equation. 2 x x + 1? . Graphing Linear Equations How can ou draw its graph? How can ou recognize a linear equation? ACTIVITY: Graphing a Linear Equation Work with a partner. a. Use the equation = + to complete the table. (Choose

More information

ACTIVITY: Frieze Patterns and Reflections. a. Is the frieze pattern a reflection of itself when folded horizontally? Explain.

ACTIVITY: Frieze Patterns and Reflections. a. Is the frieze pattern a reflection of itself when folded horizontally? Explain. . Reflections frieze pattern? How can ou use reflections to classif a Reflection When ou look at a mountain b a lake, ou can see the reflection, or mirror image, of the mountain in the lake. If ou fold

More information

Fair Game Review. Chapter 2. and y = 5. Evaluate the expression when x = xy 2. 4x. Evaluate the expression when a = 9 and b = 4.

Fair Game Review. Chapter 2. and y = 5. Evaluate the expression when x = xy 2. 4x. Evaluate the expression when a = 9 and b = 4. Name Date Chapter Fair Game Review Evaluate the epression when = and =.... 0 +. 8( ) Evaluate the epression when a = 9 and b =.. ab. a ( b + ) 7. b b 7 8. 7b + ( ab ) 9. You go to the movies with five

More information

Rotate. A bicycle wheel can rotate clockwise or counterclockwise. ACTIVITY: Three Basic Ways to Move Things

Rotate. A bicycle wheel can rotate clockwise or counterclockwise. ACTIVITY: Three Basic Ways to Move Things . Rotations object in a plane? What are the three basic was to move an Rotate A biccle wheel can rotate clockwise or counterclockwise. 0 0 0 9 9 9 8 8 8 7 6 7 6 7 6 ACTIVITY: Three Basic Was to Move Things

More information

ACTIVITY: Describing an Exponential Function

ACTIVITY: Describing an Exponential Function 6. Eponential Functions eponential function? What are the characteristics of an ACTIVITY: Describing an Eponential Function Work with a partner. The graph below shows estimates of the population of Earth

More information

Exponential Functions

Exponential Functions 6. Eponential Functions Essential Question What are some of the characteristics of the graph of an eponential function? Eploring an Eponential Function Work with a partner. Cop and complete each table

More information

Graphing Proportional Relationships

Graphing Proportional Relationships .3.3 Graphing Proportional Relationships equation = m? How can ou describe the graph of the ACTIVITY: Identifing Proportional Relationships Work with a partner. Tell whether and are in a proportional relationship.

More information

By naming a function f, you can write the function using function notation. Function notation. ACTIVITY: Matching Functions with Their Graphs

By naming a function f, you can write the function using function notation. Function notation. ACTIVITY: Matching Functions with Their Graphs 5. Function Notation represent a function? How can ou use function notation to B naming a function f, ou can write the function using function notation. f () = Function notation This is read as f of equals

More information

ACTIVITY: Representing Data by a Linear Equation

ACTIVITY: Representing Data by a Linear Equation 9.2 Lines of Fit How can ou use data to predict an event? ACTIVITY: Representing Data b a Linear Equation Work with a partner. You have been working on a science project for 8 months. Each month, ou measured

More information

4 B. 4 D. 4 F. 3. What are some common characteristics of the graphs of cubic and quartic polynomial functions?

4 B. 4 D. 4 F. 3. What are some common characteristics of the graphs of cubic and quartic polynomial functions? .1 Graphing Polnomial Functions COMMON CORE Learning Standards HSF-IF.B. HSF-IF.C.7c Essential Question What are some common characteristics of the graphs of cubic and quartic polnomial functions? A polnomial

More information

How can you enlarge or reduce a figure in the coordinate plane? Dilate. ACTIVITY: Comparing Triangles in a Coordinate Plane.

How can you enlarge or reduce a figure in the coordinate plane? Dilate. ACTIVITY: Comparing Triangles in a Coordinate Plane. . Dilations How can ou enlarge or reduce a figure in the coordinate plane? Dilate When ou have our ees checked, the optometrist sometimes dilates one or both of the pupils of our ees. ACTIVITY: Comparing

More information

ACTIVITY: Forming the Entire Coordinate Plane

ACTIVITY: Forming the Entire Coordinate Plane .5 The Coordinate Plane How can ou graph and locate points that contain negative numbers in a coordinate plane? You have alread graphed points and polgons in one part of the coordinate plane. In Activit,

More information

1.1. Parent Functions and Transformations Essential Question What are the characteristics of some of the basic parent functions?

1.1. Parent Functions and Transformations Essential Question What are the characteristics of some of the basic parent functions? 1.1 Parent Functions and Transformations Essential Question What are the characteristics of some of the basic parent functions? Identifing Basic Parent Functions JUSTIFYING CONCLUSIONS To be proficient

More information

3.5 Write and Graph Equations

3.5 Write and Graph Equations .5 Write and Graph Equations of Lines Goal p Find equations of lines. Your Notes VOCABULARY Slope-intercept form Standard form Eample Write an equation of a line from a graph Write an equation of the line

More information

Graphing f ( x) = ax 2 + c

Graphing f ( x) = ax 2 + c . Graphing f ( ) = a + c Essential Question How does the value of c affect the graph of f () = a + c? Graphing = a + c Work with a partner. Sketch the graphs of the functions in the same coordinate plane.

More information

Evaluate and Graph Polynomial Functions

Evaluate and Graph Polynomial Functions 5.2 Evaluate and Graph Polnomial Functions Before You evaluated and graphed linear and quadratic functions. Now You will evaluate and graph other polnomial functions. Wh? So ou can model skateboarding

More information

(0, 2) y = x 1 2. y = x (2, 2) y = 2x + 2

(0, 2) y = x 1 2. y = x (2, 2) y = 2x + 2 .5 Equations of Parallel and Perpendicular Lines COMMON CORE Learning Standards HSG-GPE.B.5 HSG-GPE.B. Essential Question How can ou write an equation of a line that is parallel or perpendicular to a given

More information

Lesson 5.2 Exercises, pages

Lesson 5.2 Exercises, pages Lesson 5. Eercises, pages 6 68 A. Determine whether each point is a solution of the given inequalit. a) - -16 A(-, ) In the inequalit, substitute:, L.S.: ( ) () 17 R.S. 16 Since the L.S.

More information

Polygons in the Coordinate Plane

Polygons in the Coordinate Plane . Polgons in the Coordinate Plane How can ou find the lengths of line segments in a coordinate plane? ACTIVITY: Finding Distances on a Map Work with a partner. The coordinate grid shows a portion of a

More information

Laurie s Notes. Overview of Section 6.3

Laurie s Notes. Overview of Section 6.3 Overview of Section.3 Introduction In this lesson, eponential equations are defined. Students distinguish between linear and eponential equations, helping to focus on the definition of each. A linear function

More information

Essential Question How many turning points can the graph of a polynomial function have?

Essential Question How many turning points can the graph of a polynomial function have? .8 Analzing Graphs of Polnomial Functions Essential Question How man turning points can the graph of a polnomial function have? A turning point of the graph of a polnomial function is a point on the graph

More information

Graphing Quadratic Functions

Graphing Quadratic Functions Graphing Quadratic Functions. Graphing = a. Focus of a Parabola. Graphing = a + c. Graphing = a + b + c. Comparing Linear, Eponential, and Quadratic Functions What tpe of graph is this? Sorr, no it s the

More information

= = The number system. Module. Glossary Math Tools... 33

= = The number system. Module. Glossary Math Tools... 33 - > + > < - %. < + a = - = = b in. F - - Module The number sstem Lesson Rational and Irrational Numbers........ 8.NS. Lesson ompare and Order Numbers......... 8 8.NS., 8.NS. Lesson Estimate the Value of

More information

Perimeter and Area in the Coordinate Plane

Perimeter and Area in the Coordinate Plane 1. Perimeter and Area in the Coordinate Plane COMMON CORE Learning Standard HSG-GPE.B.7 HSG-MG.A.1 LOOKING FOR STRUCTURE To be proficient in math, ou need to visualize single objects as being composed

More information

CHECK Your Understanding

CHECK Your Understanding CHECK Your Understanding. State the domain and range of each relation. Then determine whether the relation is a function, and justif our answer.. a) e) 5(, ), (, 9), (, 7), (, 5), (, ) 5 5 f) 55. State

More information

Lesson 11 Skills Maintenance. Activity 1. Model. The addition problem is = 4. The subtraction problem is 5 9 = 4.

Lesson 11 Skills Maintenance. Activity 1. Model. The addition problem is = 4. The subtraction problem is 5 9 = 4. Lesson Skills Maintenance Lesson Planner Vocabular Development -coordinate -coordinate point of origin Skills Maintenance ddition and Subtraction of Positive and Negative Integers Problem Solving: We look

More information

Piecewise Functions. Essential Question How can you describe a function that is represented by more than one equation?

Piecewise Functions. Essential Question How can you describe a function that is represented by more than one equation? COMMON CORE Learning Standards HSA-CED.A. HSA-REI.D. HSF-IF.C.7b CONSTRUCTING VIABLE ARGUMENTS.7 To be proficient in math, ou need to justif our conclusions and communicate them to others. Piecewise Functions

More information

7. f(x) = 1 2 x f(x) = x f(x) = 4 x at x = 10, 8, 6, 4, 2, 0, 2, and 4.

7. f(x) = 1 2 x f(x) = x f(x) = 4 x at x = 10, 8, 6, 4, 2, 0, 2, and 4. Section 2.2 The Graph of a Function 109 2.2 Eercises Perform each of the following tasks for the functions defined b the equations in Eercises 1-8. i. Set up a table of points that satisf the given equation.

More information

1. A(-2, 2), B(4, -2) 3 EXAMPLE. Graph the line y = Move up 3 units. Quick Check See left.

1. A(-2, 2), B(4, -2) 3 EXAMPLE. Graph the line y = Move up 3 units. Quick Check See left. -. Plan Objectives To graph lines given their equations To write equations of lines Eamples Graphing Lines in Slope- Intercept Form Graphing Lines Using Intercepts Transforming to Slope- Intercept Form

More information

7.5. Systems of Inequalities. The Graph of an Inequality. What you should learn. Why you should learn it

7.5. Systems of Inequalities. The Graph of an Inequality. What you should learn. Why you should learn it 0_0705.qd /5/05 9:5 AM Page 5 Section 7.5 7.5 Sstems of Inequalities 5 Sstems of Inequalities What ou should learn Sketch the graphs of inequalities in two variables. Solve sstems of inequalities. Use

More information

Chapter 2: Introduction to Functions

Chapter 2: Introduction to Functions Chapter 2: Introduction to Functions Lesson 1: Introduction to Functions Lesson 2: Function Notation Lesson 3: Composition of Functions Lesson 4: Domain and Range Lesson 5: Restricted Domain Lesson 6:

More information

Ready To Go On? Skills Intervention 4-1 Graphing Relationships

Ready To Go On? Skills Intervention 4-1 Graphing Relationships Read To Go On? Skills Intervention -1 Graphing Relationships Find these vocabular words in Lesson -1 and the Multilingual Glossar. Vocabular continuous graph discrete graph Relating Graphs to Situations

More information

3.4 Graphing Functions

3.4 Graphing Functions Name Class Date 3. Graphing Functions Essential Question: How do ou graph functions? Eplore Graphing Functions Using a Given Domain Resource Locker Recall that the domain of a function is the set of input

More information

ACTIVITY 9 Continued Lesson 9-2

ACTIVITY 9 Continued Lesson 9-2 Continued Lesson 9- Lesson 9- PLAN Pacing: 1 class period Chunking the Lesson Eample A Eample B #1 #3 Lesson Practice M Notes Learning Targets: Graph on a coordinate plane the solutions of a linear inequalit

More information

How can you use a graph to show the relationship between two quantities that vary directly? How can you use an equation?

How can you use a graph to show the relationship between two quantities that vary directly? How can you use an equation? .6 Direct Variation How can ou use a graph to show the relationship between two quantities that var directl? How can ou use an equation? ACTIVITY: Math in Literature Direct Variation In this lesson, ou

More information

Comparing Two Graphs. Graphing a Square Root Function. Graphing a Cube Root Function. Finding Domain and Range

Comparing Two Graphs. Graphing a Square Root Function. Graphing a Cube Root Function. Finding Domain and Range Page of 6 7.5 Graphing Square Root and Cube Root Functions What ou should learn GOAL Graph square root and cube root functions. GOAL Use square root and cube root functions to find real-life quantities,

More information

Graphs and Functions

Graphs and Functions CHAPTER Graphs and Functions. Graphing Equations. Introduction to Functions. Graphing Linear Functions. The Slope of a Line. Equations of Lines Integrated Review Linear Equations in Two Variables.6 Graphing

More information

The Sine and Cosine Functions

The Sine and Cosine Functions Lesson -5 Lesson -5 The Sine and Cosine Functions Vocabular BIG IDEA The values of cos and sin determine functions with equations = sin and = cos whose domain is the set of all real numbers. From the eact

More information

Function Notation. Essential Question How can you use function notation to represent a function?

Function Notation. Essential Question How can you use function notation to represent a function? . Function Notation Essential Question How can ou use function notation to represent a function? The notation f(), called function notation, is another name for. This notation is read as the value of f

More information

Graph and Write Equations of Hyperbolas

Graph and Write Equations of Hyperbolas TEKS 9.5 a.5, 2A.5.B, 2A.5.C Graph and Write Equations of Hperbolas Before You graphed and wrote equations of parabolas, circles, and ellipses. Now You will graph and write equations of hperbolas. Wh?

More information

3 Graphing Linear Functions

3 Graphing Linear Functions Graphing Linear Functions. Functions. Linear Functions. Function Notation. Graphing Linear Equations in Standard Form.5 Graphing Linear Equations in Slope-Intercept Form. Transformations of Graphs of Linear

More information

Essential Question What are the characteristics of the graph of the tangent function?

Essential Question What are the characteristics of the graph of the tangent function? 8.5 Graphing Other Trigonometric Functions Essential Question What are the characteristics of the graph of the tangent function? Graphing the Tangent Function Work with a partner. a. Complete the table

More information

REMARKS. 8.2 Graphs of Quadratic Functions. A Graph of y = ax 2 + bx + c, where a > 0

REMARKS. 8.2 Graphs of Quadratic Functions. A Graph of y = ax 2 + bx + c, where a > 0 8. Graphs of Quadratic Functions In an earlier section, we have learned that the graph of the linear function = m + b, where the highest power of is 1, is a straight line. What would the shape of the graph

More information

5.2 Using Intercepts

5.2 Using Intercepts Name Class Date 5.2 Using Intercepts Essential Question: How can ou identif and use intercepts in linear relationships? Resource Locker Eplore Identifing Intercepts Miners are eploring 9 feet underground.

More information

Inclination of a Line

Inclination of a Line 0_00.qd 78 /8/05 Chapter 0 8:5 AM Page 78 Topics in Analtic Geometr 0. Lines What ou should learn Find the inclination of a line. Find the angle between two lines. Find the distance between a point and

More information

Transformations of Functions. Shifting Graphs. Similarly, you can obtain the graph of. g x x 2 2 f x 2. Vertical and Horizontal Shifts

Transformations of Functions. Shifting Graphs. Similarly, you can obtain the graph of. g x x 2 2 f x 2. Vertical and Horizontal Shifts 0_007.qd /7/05 : AM Page 7 7 Chapter Functions and Their Graphs.7 Transormations o Functions What ou should learn Use vertical and horizontal shits to sketch graphs o unctions. Use relections to sketch

More information

Transformations. which the book introduces in this chapter. If you shift the graph of y 1 x to the left 2 units and up 3 units, the

Transformations. which the book introduces in this chapter. If you shift the graph of y 1 x to the left 2 units and up 3 units, the CHAPTER 8 Transformations Content Summar In Chapter 8, students continue their work with functions, especiall nonlinear functions, through further stud of function graphs. In particular, the consider three

More information

Graphing f ( x) = ax 2 + bx + c

Graphing f ( x) = ax 2 + bx + c 8.3 Graphing f ( ) = a + b + c Essential Question How can ou find the verte of the graph of f () = a + b + c? Comparing -Intercepts with the Verte Work with a partner. a. Sketch the graphs of = 8 and =

More information

Graphing square root functions. What would be the base graph for the square root function? What is the table of values?

Graphing square root functions. What would be the base graph for the square root function? What is the table of values? Unit 3 (Chapter 2) Radical Functions (Square Root Functions Sketch graphs of radical functions b appling translations, stretches and reflections to the graph of Analze transformations to identif the of

More information

The Graph Scale-Change Theorem

The Graph Scale-Change Theorem Lesson 3-5 Lesson 3-5 The Graph Scale-Change Theorem Vocabular horizontal and vertical scale change, scale factor size change BIG IDEA The graph of a function can be scaled horizontall, verticall, or in

More information

Transformations of Absolute Value Functions. Compression A compression is a. function a function of the form f(x) = a 0 x - h 0 + k

Transformations of Absolute Value Functions. Compression A compression is a. function a function of the form f(x) = a 0 x - h 0 + k - Transformations of Absolute Value Functions TEKS FOCUS VOCABULARY Compression A compression is a TEKS (6)(C) Analze the effect on the graphs of f() = when f() is replaced b af(), f(b), f( - c), and f()

More information

Functions. Name. Use an XY Coordinate Pegboard to graph each line. Make a table of ordered pairs for each line. y = x + 5 x y.

Functions. Name. Use an XY Coordinate Pegboard to graph each line. Make a table of ordered pairs for each line. y = x + 5 x y. Lesson 1 Functions Name Use an XY Coordinate Pegboard to graph each line. Make a table of ordered pairs for each line. 1. = + = + = 2 3 = 2 3 Using an XY Coordinate Pegboard, graph the line on a coordinate

More information

5.2 Graphing Polynomial Functions

5.2 Graphing Polynomial Functions Locker LESSON 5. Graphing Polnomial Functions Common Core Math Standards The student is epected to: F.IF.7c Graph polnomial functions, identifing zeros when suitable factorizations are available, and showing

More information

Name Date. In Exercises 1 6, graph the function. Compare the graph to the graph of ( )

Name Date. In Exercises 1 6, graph the function. Compare the graph to the graph of ( ) Name Date 8. Practice A In Eercises 6, graph the function. Compare the graph to the graph of. g( ) =. h =.5 3. j = 3. g( ) = 3 5. k( ) = 6. n = 0.5 In Eercises 7 9, use a graphing calculator to graph the

More information

Essential Question: How do you graph an exponential function of the form f (x) = ab x? Explore Exploring Graphs of Exponential Functions. 1.

Essential Question: How do you graph an exponential function of the form f (x) = ab x? Explore Exploring Graphs of Exponential Functions. 1. Locker LESSON 4.4 Graphing Eponential Functions Common Core Math Standards The student is epected to: F-IF.7e Graph eponential and logarithmic functions, showing intercepts and end behavior, and trigonometric

More information

8.5 Quadratic Functions and Their Graphs

8.5 Quadratic Functions and Their Graphs CHAPTER 8 Quadratic Equations and Functions 8. Quadratic Functions and Their Graphs S Graph Quadratic Functions of the Form f = + k. Graph Quadratic Functions of the Form f = - h. Graph Quadratic Functions

More information

6.1. Graphing Linear Inequalities in Two Variables. INVESTIGATE the Math. Reflecting

6.1. Graphing Linear Inequalities in Two Variables. INVESTIGATE the Math. Reflecting 6.1 Graphing Linear Inequalities in Two Variables YOU WILL NEED graphing technolog OR graph paper, ruler, and coloured pencils EXPLORE For which inequalities is (3, 1) a possible solution? How do ou know?

More information

Find Rational Zeros. has integer coefficients, then every rational zero of f has the following form: x 1 a 0. } 5 factor of constant term a 0

Find Rational Zeros. has integer coefficients, then every rational zero of f has the following form: x 1 a 0. } 5 factor of constant term a 0 .6 Find Rational Zeros TEKS A.8.B; P..D, P..A, P..B Before You found the zeros of a polnomial function given one zero. Now You will find all real zeros of a polnomial function. Wh? So ou can model manufacturing

More information

Graphing Cubic Functions

Graphing Cubic Functions Locker 8 - - - - - -8 LESSON. Graphing Cubic Functions Name Class Date. Graphing Cubic Functions Essential Question: How are the graphs of f () = a ( - h) + k and f () = ( related to the graph of f ()

More information

Name Date. using the vector 1, 4. Graph ABC. and its image. + to find the image

Name Date. using the vector 1, 4. Graph ABC. and its image. + to find the image _.1 ractice 1. Name the vector and write its component form. K J. The vertices of, 3, 1,, and 0, 1. Translate using the vector 1,. Graph and its image. are ( ) ( ) ( ) 3. Find the component form of the

More information

3.6. Transformations of Graphs of Linear Functions

3.6. Transformations of Graphs of Linear Functions . Transformations of Graphs of Linear Functions Essential Question How does the graph of the linear function f() = compare to the graphs of g() = f() + c and h() = f(c)? Comparing Graphs of Functions USING

More information

Content Standards Two-Variable Inequalities

Content Standards Two-Variable Inequalities -8 Content Standards Two-Variable Inequalities A.CED. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate aes with labels and scales.

More information

Graphing f ( x) = ax 2

Graphing f ( x) = ax 2 . Graphing f ( ) = a Essential Question What are some of the characteristics of the graph of a quadratic function of the form f () = a? Graphing Quadratic Functions Work with a partner. Graph each quadratic

More information

MATH SPEAK - TO BE UNDERSTOOD AND MEMORIZED

MATH SPEAK - TO BE UNDERSTOOD AND MEMORIZED FOM 11 T9 GRAPHING LINEAR EQUATIONS REVIEW - 1 MATH SPEAK - TO BE UNDERSTOOD AND MEMORIZED 1) -INTERCEPT = the point where the graph touches or crosses the -ais. It occurs when = 0. ) -INTERCEPT = the

More information

Investigation Recursive Toothpick Patterns

Investigation Recursive Toothpick Patterns Investigation Recursive Toothpick Patterns Name Period Date You will need: a bo of toothpicks In this investigation ou will learn to create and appl recursive sequences b modeling them with puzzle pieces

More information

Fair Game Review. Chapter 11. Name Date. Reflect the point in (a) the x-axis and (b) the y-axis. 2. ( 2, 4) 1. ( 1, 1 ) 3. ( 3, 3) 4.

Fair Game Review. Chapter 11. Name Date. Reflect the point in (a) the x-axis and (b) the y-axis. 2. ( 2, 4) 1. ( 1, 1 ) 3. ( 3, 3) 4. Name Date Chapter Fair Game Review Reflect the point in (a) the -ais and (b) the -ais.. (, ). (, ). (, ). (, ) 5. (, ) 6. (, ) Copright Big Ideas Learning, LLC Name Date Chapter Fair Game Review (continued)

More information

Graphing Absolute Value Functions. Objectives To graph an absolute value function To translate the graph of an absolute value function

Graphing Absolute Value Functions. Objectives To graph an absolute value function To translate the graph of an absolute value function 5-8 CC-0 CC-6 Graphing Absolute Value Functions Content Standards F.BF.3 Identif the effect on the graph of replacing f () b f () k, kf (), f (k), and f ( k) for specific values of k (both positive and

More information

5.4 Direct Variation - NOTES

5.4 Direct Variation - NOTES Name Class Date 5.4 Direct Variation - NOTES Essential Question: What is direct variation? Eplore A1.2.D write and solve equations involving direct variation Recognizing Direct Variation Recipes give the

More information

Graphing Quadratics: Vertex and Intercept Form

Graphing Quadratics: Vertex and Intercept Form Algebra : UNIT Graphing Quadratics: Verte and Intercept Form Date: Welcome to our second function famil...the QUADRATIC FUNCTION! f() = (the parent function) What is different between this function and

More information

Chapter at a Glance FLORIDA. Benchmark Lesson Worktext CHAPTER 3 CHAPTER 3. Student Textbook. Chapter 3 Graphs and Functions 49.

Chapter at a Glance FLORIDA. Benchmark Lesson Worktext CHAPTER 3 CHAPTER 3. Student Textbook. Chapter 3 Graphs and Functions 49. Graphs and Functions FLORIDA CHAPTER 3 Name Class Date Chapter at a Glance Copright b Holt McDougal. All rights reserved. Benchmark Lesson Worktet Student Tetbook Remember It? 51 5 Rev. MA.7.G..3 3-1 Ordered

More information

3-6 Lines in the Coordinate Plane

3-6 Lines in the Coordinate Plane 3-6 Lines in the Coordinate Plane Warm Up Lesson Presentation Lesson Quiz Geometry Warm Up Substitute the given values of m, x, and y into the equation y = mx + b and solve for b. 1. m = 2, x = 3, and

More information

Rotations. Essential Question How can you rotate a figure in a coordinate plane?

Rotations. Essential Question How can you rotate a figure in a coordinate plane? 11.3 Rotations Essential Question How can ou rotate a figure in a coordinate plane? Rotating a Triangle in a oordinate lane ONSTRUTING VILE RGUMENTS To be proficient in math, ou need to use previousl established

More information

Identify and graph ordered pairs on a coordinate grid.

Identify and graph ordered pairs on a coordinate grid. Ordered Pairs Teacher Notes Objective Identif and graph ordered pairs on a coordinate grid. Use these worksheets if students have trouble graphing on the coordinate plane graphing proportional relationships

More information

STRAND G: Relations, Functions and Graphs

STRAND G: Relations, Functions and Graphs UNIT G Using Graphs to Solve Equations: Tet STRAND G: Relations, Functions and Graphs G Using Graphs to Solve Equations Tet Contents * * Section G. Solution of Simultaneous Equations b Graphs G. Graphs

More information

Unit 5 Lesson 2 Investigation 1

Unit 5 Lesson 2 Investigation 1 Name: Investigation 1 Modeling Rigid Transformations CPMP-Tools Computer graphics enable designers to model two- and three-dimensional figures and to also easil manipulate those figures. For eample, interior

More information

Does the table or equation represent a linear or nonlinear function? Explain.

Does the table or equation represent a linear or nonlinear function? Explain. Chapter Review Dnamic Solutions available at BigIdeasMath.com. Functions (pp. 0 0) Determine whether the relation is a function. Eplain. Ever input has eactl one output. Input, 5 7 9 Output, 5 9 So, the

More information

Using a Table of Values to Sketch the Graph of a Polynomial Function

Using a Table of Values to Sketch the Graph of a Polynomial Function A point where the graph changes from decreasing to increasing is called a local minimum point. The -value of this point is less than those of neighbouring points. An inspection of the graphs of polnomial

More information

3x 4y 2. 3y 4. Math 65 Weekly Activity 1 (50 points) Name: Simplify the following expressions. Make sure to use the = symbol appropriately.

3x 4y 2. 3y 4. Math 65 Weekly Activity 1 (50 points) Name: Simplify the following expressions. Make sure to use the = symbol appropriately. Math 65 Weekl Activit 1 (50 points) Name: Simplif the following epressions. Make sure to use the = smbol appropriatel. Due (1) (a) - 4 (b) ( - ) 4 () 8 + 5 6 () 1 5 5 Evaluate the epressions when = - and

More information

Check Skills You ll Need (For help, go to Lesson 1-2.) Evaluate each expression for the given value of x.

Check Skills You ll Need (For help, go to Lesson 1-2.) Evaluate each expression for the given value of x. A_3eSE_00X 0/6/005 :3 AM Page - Eploring Eponential Models Lesson Preview What You ll Learn To model eponential growth To model eponential deca... And Wh To model a car s depreciation, as in Eample 6 Check

More information

5 and Parallel and Perpendicular Lines

5 and Parallel and Perpendicular Lines Ch 3: Parallel and Perpendicular Lines 3 1 Properties of Parallel Lines 3 Proving Lines Parallel 3 3 Parallel and Perpendicular Lines 3 Parallel Lines and the Triangle Angles Sum Theorem 3 5 The Polgon

More information

Learning Objectives for Section Graphs and Lines. Cartesian coordinate system. Graphs

Learning Objectives for Section Graphs and Lines. Cartesian coordinate system. Graphs Learning Objectives for Section 3.1-2 Graphs and Lines After this lecture and the assigned homework, ou should be able to calculate the slope of a line. identif and work with the Cartesian coordinate sstem.

More information

Name Date. Modeling with Linear Functions For use with Exploration 1.3

Name Date. Modeling with Linear Functions For use with Exploration 1.3 1.3 Modeling with Linear Functions For use with Exploration 1.3 Essential Question How can ou use a linear function to model and analze a real-life situation? 1 EXPLORATION: Modeling with a Linear Function

More information

Section Graphs and Lines

Section Graphs and Lines Section 1.1 - Graphs and Lines The first chapter of this text is a review of College Algebra skills that you will need as you move through the course. This is a review, so you should have some familiarity

More information

2-3. Attributes of Absolute Value Functions. Key Concept Absolute Value Parent Function f (x)= x VOCABULARY TEKS FOCUS ESSENTIAL UNDERSTANDING

2-3. Attributes of Absolute Value Functions. Key Concept Absolute Value Parent Function f (x)= x VOCABULARY TEKS FOCUS ESSENTIAL UNDERSTANDING - Attributes of Absolute Value Functions TEKS FOCUS TEKS ()(A) Graph the functions f() =, f() =, f() =, f() =,f() = b, f() =, and f() = log b () where b is,, and e, and, when applicable, analze the ke

More information

4.1 The Coordinate Plane

4.1 The Coordinate Plane 4. The Coordinate Plane Goal Plot points in a coordinate plane. VOCABULARY Coordinate plane Origin -ais -ais Ordered pair -coordinate -coordinate Quadrant Scatter plot Copright McDougal Littell, Chapter

More information

LESSON 3.1 INTRODUCTION TO GRAPHING

LESSON 3.1 INTRODUCTION TO GRAPHING LESSON 3.1 INTRODUCTION TO GRAPHING LESSON 3.1 INTRODUCTION TO GRAPHING 137 OVERVIEW Here s what ou ll learn in this lesson: Plotting Points a. The -plane b. The -ais and -ais c. The origin d. Ordered

More information

Geometric Sequences 6.7. ACTIVITY: Describing Calculator Patterns. How are geometric sequences used to. describe patterns?

Geometric Sequences 6.7. ACTIVITY: Describing Calculator Patterns. How are geometric sequences used to. describe patterns? 6.7 Geometric Sequences describe patterns? How are geometric sequences used to ACTIVITY: Describing Calculator Patterns Work with a partner. Enter the keystrokes on a calculator and record the results

More information

Why? Identify Functions A function is a relationship between input and output. In a 1 function, there is exactly one output for each input.

Why? Identify Functions A function is a relationship between input and output. In a 1 function, there is exactly one output for each input. Functions Stopping Distance of a Passenger Car Then You solved equations with elements from a replacement set. (Lesson -5) Now Determine whether a relation is a function. Find function values. Wh? The

More information

1. y = f(x) y = f(x + 3) 3. y = f(x) y = f(x 1) 5. y = 3f(x) 6. y = f(3x) 7. y = f(x) 8. y = f( x) 9. y = f(x 3) + 1

1. y = f(x) y = f(x + 3) 3. y = f(x) y = f(x 1) 5. y = 3f(x) 6. y = f(3x) 7. y = f(x) 8. y = f( x) 9. y = f(x 3) + 1 .7 Transformations.7. Eercises To see all of the help resources associated with this section, click OSttS Chapter b. Suppose (, ) is on the graph of = f(). In Eercises - 8, use Theorem.7 to find a point

More information

6. 4 Transforming Linear Functions

6. 4 Transforming Linear Functions Name Class Date 6. Transforming Linear Functions Essential Question: What are the was in which ou can transform the graph of a linear function? Resource Locker Eplore 1 Building New Linear Functions b

More information

Chapter 3. Exponential and Logarithmic Functions. Selected Applications

Chapter 3. Exponential and Logarithmic Functions. Selected Applications Chapter Eponential and Logarithmic Functions. Eponential Functions and Their Graphs. Logarithmic Functions and Their Graphs. Properties of Logarithms. Solving Eponential and Logarithmic Equations.5 Eponential

More information

Online Homework Hints and Help Extra Practice

Online Homework Hints and Help Extra Practice Evaluate: Homework and Practice Use a graphing calculator to graph the polnomial function. Then use the graph to determine the function s domain, range, and end behavior. (Use interval notation for the

More information

4.6 Graphs of Other Trigonometric Functions

4.6 Graphs of Other Trigonometric Functions .6 Graphs of Other Trigonometric Functions Section.6 Graphs of Other Trigonometric Functions 09 Graph of the Tangent Function Recall that the tangent function is odd. That is, tan tan. Consequentl, the

More information

Quadratic Inequalities

Quadratic Inequalities TEKS FCUS - Quadratic Inequalities VCABULARY TEKS ()(H) Solve quadratic inequalities. TEKS ()(E) Create and use representations to organize, record, and communicate mathematical ideas. Representation a

More information

5 8 ). a. Which operation is done first, subtraction or addition? a. Which operation is done first, addition or multiplication?

5 8 ). a. Which operation is done first, subtraction or addition? a. Which operation is done first, addition or multiplication? 7-1 Homework 1 Consider the expression - ( 3 4 + 5 ). a. Which operation is done first, subtraction or addition? b. Write the computation in words. Consider the expression 4.5 + 6 0.1. a. Which operation

More information

Ready To Go On? Skills Intervention 3-1 Using Graphs and Tables to Solve Linear Systems

Ready To Go On? Skills Intervention 3-1 Using Graphs and Tables to Solve Linear Systems Read To Go On? Skills Intervention 3-1 Using Graphs and Tables to Solve Linear Sstems Find these vocabular words in Lesson 3-1 and the Multilingual Glossar. Vocabular sstem of equations linear sstem consistent

More information

Math 1050 Lab Activity: Graphing Transformations

Math 1050 Lab Activity: Graphing Transformations Math 00 Lab Activit: Graphing Transformations Name: We'll focus on quadratic functions to eplore graphing transformations. A quadratic function is a second degree polnomial function. There are two common

More information

Slope is the ratio of the rise, or the vertical change, to the run, or the horizontal change. A greater ratio indicates a steeper slope.

Slope is the ratio of the rise, or the vertical change, to the run, or the horizontal change. A greater ratio indicates a steeper slope. 7 NAME DATE PERID Stud Guide Pages 84 89 Slope Slope is the ratio of the rise, or the vertical change, to the run, or the horizontal change. A greater ratio indicates a steeper slope. A tpical ski mountain

More information

More Coordinate Graphs. How do we find coordinates on the graph?

More Coordinate Graphs. How do we find coordinates on the graph? Lesson Problem Solving: More Coordinate Graphs Problem Solving: More Coordinate Graphs How do we find coordinates on the graph? We use coordinates to find where the dot goes on the coordinate graph. From

More information

Graph General Rational Functions. }} q(x) bn x n 1 b n 2 1. p(x) 5 a m x m 1 a m 2 1

Graph General Rational Functions. }} q(x) bn x n 1 b n 2 1. p(x) 5 a m x m 1 a m 2 1 TEKS 8.3 A.0.A, A.0.B, A.0.C, A.0.F Graph General Rational Functions Before You graphed rational functions involving linear polnomials. Now You will graph rational functions with higher-degree polnomials.

More information