Graphing Transformations Techniques -- Team Project Packet A
|
|
|
- Gwendolyn Lloyd
- 5 years ago
- Views:
Transcription
1 Name Course Days/Start Time Graphing Transformations Techniques -- Team Project Packet A This packet is to be completed by Student A working alone. It should be completed before Students A and B work together to complete Packet AB. Problem A1 Use the Graphing Techniques: Transformations -- Characteristics Worksheet to solve the problem. Write the function whose graph is the graph of y = x, but is shifted to the right 7 units. Problem A2 Use the Graphing Techniques: Transformations -- Characteristics Worksheet to solve the problem. Use your knowledge of Graphing Techniques: Transformations to complete the missing table of coordinates. When graphed, an equation/function f(x) contains the points x y Based on that data, what are the corresponding points on the equation/function f(x + 3)? x y Final Answer: (Complete the blank table above) 1
2 Problem A3 Use the Graphing Techniques: Transformations -- Characteristics Worksheet to solve the problem. When you start with the library function whose graph contains the points and you transform it into a new function whose graph contains the points this represents which type of transformation? (Circle one.) A horizontal shift right B horizontal shift left C vertical shift up D vertical shift down Problem A4 Use the Graphing Techniques: Transformations -- Characteristics Worksheet to solve the problem. Use your knowledge of Graphing Techniques: Transformations to complete the missing table of coordinates. 3 When graphed, the equation y = x contains the points x y What are the corresponding points when graphing = x x y 1? Final Answer: (Complete the blank table above) 2
3 Problem A5 Use the Graphing Techniques: Transformations -- Characteristics Worksheet to solve the problem. One of the library functions has been transformed to create the graph. Write the equation of the function that matches the graph. Problem A6 Use the Graphing Techniques: Transformations -- Characteristics Worksheet to solve the problem. When you start with the library function whose graph contains the points and you transform it into a new function whose graph contains the points this represents which type of transformation? (Circle one.) A horizontal shift right B horizontal shift left C vertical shift up D vertical shift down 3
4 Problem A7 Consider the graph of f(x) on the right. Use the graph of f to complete the table and graph P(x) = f(x 1) on the same grid. f(x) P(x) = f(x-1) Image Copyright 2013 Pearson Education Step 2: Identify what you are being asked to create: (Circle Two) Final Answer: (Complete the table above and create the new graph on the same grid) Problem A8 Use the Graphing Techniques: Transformations -- Characteristics Worksheet to solve the problem. Write the function whose graph is the graph of y = x, but is shifted to the left 8 units. 4
5 Problem A9 Use the Graphing Techniques: Transformations -- Characteristics Worksheet to solve the problem. Write the function whose graph is the graph of y = x, but is shifted up 8 units. Problem A10 What do you notice about your answers to Problems A8 and A9? Why did this happen? What did you notice?: Why did this happen? (Fill in the blanks in the sentences below.) A line extends forever in two directions. So when a line with a positive slope is moved to the left, it also appears to be moving. And when a line with a positive slope is moved up, it also appears to be moving. Problem A11 Use the Graphing Techniques: Transformations -- Characteristics Worksheet to solve the problem. Write the function whose graph is the graph of y = x, but is compressed towards the y-axis using an a value of 4. 5
6 Problem A12 Use the Graphing Techniques: Transformations -- Characteristics Worksheet to solve the problem. Use your knowledge of Graphing Techniques: Transformations to complete the missing table of coordinates. When graphed, an equation/function f(x) contains the points x y Based on that data, what are the corresponding points on the equation/function f( 1 2 x)? x y Final Answer: (Complete the blank table above) Problem A13 Use the Graphing Techniques: Transformations -- Characteristics Worksheet to solve the problem. When you start with the library function whose graph contains the points and you transform it into a new function whose graph contains the points this represents which type of transformation? (Circle one.) A horizontal compression B vertical compression C horizontal stretch D vertical stretch 6
7 Problem A14 Use the Graphing Techniques: Transformations -- Characteristics Worksheet to solve the problem. Use your knowledge of Graphing Techniques: Transformations to complete the missing table of coordinates. 3 When graphed, the equation y = x contains the points x y What are the corresponding points when graphing = x? x y Final Answer: (Complete the blank table above) Problem A15 Use the Graphing Techniques: Transformations -- Characteristics Worksheet to solve the problem. One of the library functions has been transformed to create the graph. Write the equation of the function that matches the graph. 7
8 Problem A16 Use the Graphing Techniques: Transformations -- Characteristics Worksheet to solve the problem. When you start with the library function whose graph contains the points and you transform it into a new function whose graph contains the points this represents which type of transformation? (Circle one.) A horizontal compression B vertical compression C horizontal stretch D vertical stretch 8
Graphing Transformations Techniques -- Team Project Packet B
Name Course Days/Start Time Graphing Transformations Techniques -- Team Project Packet B This packet is to be completed by Student B working alone. It should be completed before Students A and B work together
Graphing Transformations Techniques -- Partner Pairs Project Packet A
Name Course Days/Times Graphing Transformations Techniques -- Partner Pairs Project Packet A This packet is to be completed by Student A working alone. It should be completed before Students A and B work
September 18, B Math Test Chapter 1 Name: x can be expressed as: {y y 0, y R}.
September 8, 208 62B Math Test Chapter Name: Part : Objective Questions [ mark each, total 2 marks]. State whether each of the following statements is TRUE or FALSE a) The mapping rule (x, y) (-x, y) represents
Graphs and transformations 4G
Graphs and transformations 4G a f(x + ) is a translation by one unit to the left. d A (0, ), B ( ),0, C (, 4), D (, 0) A (, ), B (0, 0), C (, 4), D (5, 0) e f(x) is a stretch with scale factor b f(x) 4
Sections Transformations
MCR3U Sections 1.6 1.8 Transformations Transformations: A change made to a figure or a relation such that it is shifted or changed in shape. Translations, reflections and stretches/compressions are types
Graphs and transformations, Mixed Exercise 4
Graphs and transformations, Mixed Exercise 4 a y = x (x ) 0 = x (x ) So x = 0 or x = The curve crosses the x-axis at (, 0) and touches it at (0, 0). y = x x = x( x) As a = is negative, the graph has a
Situation #1: Translating Functions Prepared at University of Georgia William Plummer EMAT 6500 Date last revised: July 28, 2013
Situation #1: Translating Functions Prepared at University of Georgia William Plummer EMAT 6500 Date last revised: July 28, 2013 Prompt An Algebra class is discussing the graphing of quadratic functions
6B Quiz Review Learning Targets ,
6B Quiz Review Learning Targets 5.10 6.3, 6.5-6.6 Key Facts Double transformations when more than one transformation is applied to a graph o You can still use our transformation rules to identify which
Graphing Techniques and Transformations. Learning Objectives. Remarks
Graphing Techniques and Transformations Learning Objectives 1. Graph functions using vertical and horizontal shifts 2. Graph functions using compressions and stretches. Graph functions using reflections
transformation: alters the equation and any combination of the location, shape, and orientation of the graph
Chapter 1: Function Transformations Section 1.1: Horizontal and Vertical Translations transformation: alters the equation and any combination of the location, shape, and orientation of the graph mapping:
The x-intercept can be found by setting y = 0 and solving for x: 16 3, 0
y=-3/4x+4 and y=2 x I need to graph the functions so I can clearly describe the graphs Specifically mention any key points on the graphs, including intercepts, vertex, or start/end points. What is the
Lesson #6: Basic Transformations with the Absolute Value Function
Lesson #6: Basic Transformations with the Absolute Value Function Recall: Piecewise Functions Graph:,, What parent function did this piecewise function create? The Absolute Value Function Algebra II with
Algebra II Chapter 3 Test Review Standards/Goals: F.IF.1:
1 Algebra II Chapter 3 Test Review Standards/Goals: F.IF.1: o o I can understand what a relation and a function is. I can understand that a function assigns to each element of a domain, EXACTLY one element
Practice Test (page 391) 1. For each line, count squares on the grid to determine the rise and the run. Use slope = rise
Practice Test (page 91) 1. For each line, count squares on the grid to determine the rise and the. Use slope = rise 4 Slope of AB =, or 6 Slope of CD = 6 9, or Slope of EF = 6, or 4 Slope of GH = 6 4,
Core Mathematics 1 Transformations of Graphs
Regent College Maths Department Core Mathematics 1 Transformations of Graphs Transformations of Graphs September 2011 C1 Note Knowledge of the effect of simple transformations on the graph of y f( x)
Linear Functions. College Algebra
Linear Functions College Algebra Linear Function A linear function is a function whose graph is a straight line. Linear functions can be written in the slope-intercept form of a line: f(x) = mx + b where
Did You Find a Parking Space?
Lesson.4 Skills Practice Name Date Did You Find a Parking Space? Parallel and Perpendicular Lines on the Coordinate Plane Vocabulary Complete the sentence. 1. The point-slope form of the equation of the
Sect Graphing Techniques: Transformations
Sect. - Graphing Techniques: Transformations Recall the general shapes of each of the following basic functions and their properties: Identity Function Square Function f(x) = x f(x) = x - - - - - - - -
Warm - Up. Sunday, February 1, HINT: plot points first then connect the dots. Draw a graph with the following characteristics:
Warm - Up Sunday, February 1, 2015 Draw a graph with the following characteristics: Maximums at (-3,4) and (2,2) Minimum at (-1,-3) X intercepts at (-4,0), (-2,0), (1,0), and (3,0) Y intercept at (0,-2)
Rationale. Instructional Task
A-E Strand(s): Algebra. Sample Courses: Middle School Course 2, Middle School One-Year Advanced Course, Integrated 3, and Algebra II. Topic/Expectation A.C.1 Elementary functions g. Explain, illustrate
Notes Rules for Transformations of Functions If f x is the original functions, a > 0 and c > 0.
9.1.2 Parabola Investigation Do Now 1. Vertical means and horizontal is. 2. Another word for compress is. 3. Given the statement 0 < a < 1, a represents numbers like 4. Given the statement a > 1, a represents
Section 1.6 & 1.7 Parent Functions and Transformations
Math 150 c Lynch 1 of 8 Section 1.6 & 1.7 Parent Functions and Transformations Piecewise Functions Example 1. Graph the following piecewise functions. 2x + 3 if x < 0 (a) f(x) = x if x 0 1 2 (b) f(x) =
3. parallel: (b) and (c); perpendicular (a) and (b), (a) and (c)
SECTION 1.1 1. Plot the points (0, 4), ( 2, 3), (1.5, 1), and ( 3, 0.5) in the Cartesian plane. 2. Simplify the expression 13 7 2. 3. Use the 3 lines whose equations are given. Which are parallel? Which
Amphitheater School District End Of Year Algebra II Performance Assessment Review
Amphitheater School District End Of Year Algebra II Performance Assessment Review This packet is intended to support student preparation and review for the Algebra II course concepts for the district common
Transformations with Quadratic Functions KEY
Algebra Unit: 05 Lesson: 0 TRY THIS! Use a calculator to generate a table of values for the function y = ( x 3) + 4 y = ( x 3) x + y 4 Next, simplify the function by squaring, distributing, and collecting
Checkpoint: Assess Your Understanding, pages
Checkpoint: Assess Your Understanding, pages 13 1 3.1 1. Multiple Choice The graph of 3 3 is translated units right and 5 units down. What is an equation of the translation image? A. =-3( + ) 3 + 9 B.
Honors Algebra 2 Function Transformations Discovery
Honors Algebra Function Transformations Discovery Name: Date: Parent Polynomial Graphs Using an input-output table, make a rough sketch and compare the graphs of the following functions. f x x. f x x.
a translation by c units a translation by c units
1.6 Graphical Transformations Introducing... Translations 1.) Set your viewing window to [-5,5] by [-5,15]. 2.) Graph the following functions: y 1 = x 2 y 2 = x 2 + 3 y 3 = x 2 + 1 y 4 = x 2-2 y 5 = x
Name Class Date. subtract 3 from each side. w 5z z 5 2 w p - 9 = = 15 + k = 10m. 10. n =
Reteaching Solving Equations To solve an equation that contains a variable, find all of the values of the variable that make the equation true. Use the equalit properties of real numbers and inverse operations
2. The diagram shows part of the graph of y = a (x h) 2 + k. The graph has its vertex at P, and passes through the point A with coordinates (1, 0).
Quadratics Vertex Form 1. Part of the graph of the function y = d (x m) + p is given in the diagram below. The x-intercepts are (1, 0) and (5, 0). The vertex is V(m, ). (a) Write down the value of (i)
Replacing f(x) with k f(x) and. Adapted from Walch Education
Replacing f(x) with k f(x) and f(k x) Adapted from Walch Education Graphing and Points of Interest In the graph of a function, there are key points of interest that define the graph and represent the characteristics
Final Exam Review Algebra Semester 1
Final Exam Review Algebra 015-016 Semester 1 Name: Module 1 Find the inverse of each function. 1. f x 10 4x. g x 15x 10 Use compositions to check if the two functions are inverses. 3. s x 7 x and t(x)
Mini-Lecture 3.1 Graphing Equations
Copyright 0 Pearson Education, Inc. Mini-Lecture. Graphing Equations. Plot ordered pairs.. Determine whether an ordered pair of numbers is a solution to an equation in two variables.. Graph linear equations.
Mini-Project 1: The Library of Functions and Piecewise-Defined Functions
Name Course Days/Start Time Mini-Project 1: The Library of Functions and Piecewise-Defined Functions Part 2: Piecewise-Defined Functions A piecewise-defined function is two or more functions combined into
2.4. Rates of Change and Tangent Lines. Copyright 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall
2.4 Rates of Change and Tangent Lines Copyright 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall What you ll learn about Average Rates of Change Tangent to a Curve Slope of a Curve Normal
Transformation a shifting or change in shape of a graph
1.1 Horizontal and Vertical Translations Frieze Patterns Transformation a shifting or change in shape of a graph Mapping the relating of one set of points to another set of points (ie. points on the original
Amplifying an Instructional Task Algebra II Example
Original Task The student is expected to write the equation of a parabola using given attributes, including vertex, focus, directrix, axis of symmetry, and direction of opening. A(4)(B) Write the equations
Important!!! First homework is due on Monday, September 26 at 8:00 am.
Important!!! First homework is due on Monday, September 26 at 8:00 am. You can solve and submit the homework on line using webwork: http://webwork.dartmouth.edu/webwork2/m3cod/. If you do not have a user
F.BF.B.3: Graphing Polynomial Functions
F.BF.B.3: Graphing Polynomial Functions 1 Given the graph of the line represented by the equation f(x) = 2x + b, if b is increased by 4 units, the graph of the new line would be shifted 4 units 1) right
Direction Fields; Euler s Method
Direction Fields; Euler s Method It frequently happens that we cannot solve first order systems dy (, ) dx = f xy or corresponding initial value problems in terms of formulas. Remarkably, however, this
Review for test 2. Graphs of functions (vertical shifts, horizontal shifts, compression, stretching): Given the graph of y=f(x), and c >0
Review for test 2 Graphs of functions (vertical shifts, horizontal shifts, compression, stretching): Given the graph of y=f(x), and c >0 a) The graph of y=f(x-c) is obtained by b) The graph of y=f(x+c)
Nelson Functions 11 Errata
Nelson Functions 11 Errata 1: Introduction to Functions Location Question Correct Answer Getting Started 6a Graph is correct but vertex and axis of symmetry are not labelled. Add blue point labelled (in
MAT 106: Trigonometry Brief Summary of Function Transformations
MAT 106: Trigonometry Brief Summary of Function Transformations The sections below are intended to provide a brief overview and summary of the various types of basic function transformations covered in
Proof of Identities TEACHER NOTES MATH NSPIRED. Math Objectives. Vocabulary. About the Lesson. TI-Nspire Navigator System
Math Objectives Students will be able to interpret reciprocal, negative angle, cofunction, and Pythagorean identities in terms of the graphs of the trigonometric functions involved Students will be able
Assignments for Algebra 1 Unit 9 Quadratics, Part 1
Name: Assignments for Algebra 1 Unit 9 Quadratics, Part 1 Day 1, Quadratic Transformations: p.1-2 Day 2, Vertex Form of Quadratics: p. 3 Day 3, Solving Quadratics: p. 4-5 Day 4, No Homework (be sure you
Caryn Loves Math 1
2011-2015 Caryn Loves Math 1 Piecewise-defined Functions Bundles By Caryn White Table of Contents Copy Right Information:... 3 Worksheets... 4 Evaluating Piecewise Functions (1)... 5 Evaluating Piecewise
1-8 Exploring Transformations
1-8 Exploring Transformations Warm Up Lesson Presentation Lesson Quiz 2 Warm Up Plot each point. D 1. A(0,0) 2. B(5,0) 3. C( 5,0) 4. D(0,5) 5. E(0, 5) 6. F( 5, 5) C A F E B Objectives Apply transformations
Obtaining Information from a Function s Graph.
Obtaining Information from a Function s Graph Summary about using closed dots, open dots, and arrows on the graphs 1 A closed dot indicate that the graph does not extend beyond this point and the point
Section 4.1 Review of Quadratic Functions and Graphs (3 Days)
Integrated Math 3 Name What can you remember before Chapter 4? Section 4.1 Review of Quadratic Functions and Graphs (3 Days) I can determine the vertex of a parabola and generate its graph given a quadratic
Basic Transformations
Basic Transformations www.math40s.com 90 Part I: Vertical Stretches Vertical Stretches: A vertical stretch is represented by the form y = af(x), where a is the vertical stretch factor. Example 1: Stretch
Algebra 2 Chapter Relations and Functions
Algebra 2 Chapter 2 2.1 Relations and Functions 2.1 Relations and Functions / 2.2 Direct Variation A: Relations What is a relation? A of items from two sets: A set of values and a set of values. What does
Objectives. Vocabulary. 1-1 Exploring Transformations
Warm Up Plot each point. D Warm Up Lesson Presentation Lesson Quiz 1. A(0,0) 2. B(5,0) 3. C( 5,0) 4. D(0,5) C A B 5. E(0, 5) 6. F( 5, 5) F E Algebra 2 Objectives Apply transformations to points and sets
S56 (5.1) Graphs of Functions.notebook September 22, 2016
Daily Practice 8.9.2016 Q1. Write in completed square form y = 3x 2-18x + 4 Q2. State the equation of the line that passes through (2, 3) and is parallel to the x - axis Q1. If f(x) = 3x + k and g(x) =
Butterflies, Pinwheels, and Wallpaper
Butterflies, Pinwheels, and Wallpaper Day Topic Homework IXL Grade 1 Inv 1.1 Inv 1/ACE # 1-6 2 Inv 1.2 Inv 1/ACE # 19-20 3 Inv 1.3 Inv 1/ACE # 8-12 (all part a only!) 4 Inv 1.4 Inv 1/ACE # 14-17, 30-34,
1.2 Reflections and Stretches
Chapter Part : Reflections.2 Reflections and Stretches Pages 6 3 Investigating a reflection in the x axis:. a) Complete the following table for and sketch on the axis provided. x 2 0 2 y b) Now sketch
REVIEW FOR THE FIRST SEMESTER EXAM
Algebra II Honors @ Name Period Date REVIEW FOR THE FIRST SEMESTER EXAM You must NEATLY show ALL of your work ON SEPARATE PAPER in order to receive full credit! All graphs must be done on GRAPH PAPER!
Section 6.2 Graphs of the Other Trig Functions
Section 62 Graphs of the Other Trig Functions 369 Section 62 Graphs of the Other Trig Functions In this section, we will explore the graphs of the other four trigonometric functions We ll begin with the
AP Calculus AB Summer Review Packet
AP Calculus AB Summer Review Packet Mr. Burrows Mrs. Deatherage 1. This packet is to be handed in to your Calculus teacher on the first day of the school year. 2. All work must be shown on separate paper
Butterflies, Pinwheels, and Wallpaper
Butterflies, Pinwheels, and Wallpaper Day Topic Homework Grade 1 Intro Day start work on notes, vocab, and ACE questions 2 Inv 1/ACE # 1-6, 8-12, 14-17, 19-20, 30-34, 36a, 37a due by Friday 1/9 at 3:15
CHAPTER 2: More on Functions
MAT 171 Precalculus Algebra Dr. Claude Moore Cape Fear Community College CHAPTER 2: More on Functions 2.1 Increasing, Decreasing, and Piecewise Functions; Applications 2.2 The Algebra of Functions 2.3
2. Find the midpoint between the two points and. a. (3, -6) b. (-1, -13) c. d. e.
Precalculus with Limits (Larson 2 nd ed.) Chapter 1 Mid-Term Exam Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Find the distance between the
Transformation of Functions You should know the graph of the following basic functions: f(x) = x 2. f(x) = x 3
Transformation of Functions You should know the graph of the following basic functions: f(x) = x 2 f(x) = x 3 f(x) = 1 x f(x) = x f(x) = x If we know the graph of a basic function f(x), we can draw the
4) Simplify 5( 6) Simplify. 8) Solve 1 x 2 4
Algebra Summer Assignment 1) Simplify x 4y 10 x ) Simplify 4y 6x 3( x y) 3) Simplify 1 3 ( x 3) 4) Simplify 5( x 9x) (3x 4) 7 5) Simplify ( x 3)( x ) 6) Simplify ( x 4) 3 7) Simplify ( 5x 8)(4x 1) 8) Solve
2-5 Graphing Special Functions. Graph each function. Identify the domain and range. SOLUTION:
Graph each function Identify the domain and range Write the piecewise-defined function shown in each graph 1 3 The left portion of the graph is the line g(x) = x + 4 There is an open circle at ( 2, 2),
Section a) f(x-3)+4 = (x 3) the (-3) in the parenthesis moves right 3, the +4 moves up 4
Section 4.3 1a) f(x-3)+4 = (x 3) 2 + 4 the (-3) in the parenthesis moves right 3, the +4 moves up 4 Answer 1a: f(x-3)+4 = (x 3) 2 + 4 The graph has the same shape as f(x) = x 2, except it is shifted right
2.1. Rectangular Coordinates and Graphs. 2.1 Rectangular Coordinates and Graphs 2.2 Circles 2.3 Functions 2.4 Linear Functions. Graphs and Functions
2 Graphs and Functions 2 Graphs and Functions 2.1 Rectangular Coordinates and Graphs 2.2 Circles 2.3 Functions 2.4 Linear Functions Sections 2.1 2.4 2008 Pearson Addison-Wesley. All rights reserved Copyright
Lesson 5.2: Transformations of Sinusoidal Functions (Sine and Cosine)
Lesson 5.2: Transformations of Sinusoidal Functions (Sine and Cosine) Reflections Horizontal Translation (c) Vertical Translation (d) Remember: vertical stretch horizontal stretch 1 Part A: Reflections
Graphs of the Circular Functions. Copyright 2017, 2013, 2009 Pearson Education, Inc.
4 Graphs of the Circular Functions Copyright 2017, 2013, 2009 Pearson Education, Inc. 1 4.3 Graphs of the Tangent and Cotangent Functions Graph of the Tangent Function Graph of the Cotangent Function Techniques
2018 PRE-CAL PAP SUMMER REVIEW
NAME: DATE: 018 PRE-CAL PAP SUMMER REVIEW ***Due August 1 st *** Email To: Schmidtam@needvilleisd.com or Drop off & put in my box at the High School You can see this site for help: https://www.khanacademy.org/math/algebra
MATH 111 QUADRATICS WORKSHEET. Solution. We can put f(x) into vertex form by completing the square:
MATH 111 QUADRATICS WORKSHEET BLAKE FARMAN UNIVERSITY OF SOUTH CAROLINA Name: Let f(x) = 3x 2 + 6x + 9. Use this function to answer questions Problems 1-3. 1. Write f(x) in vertex form. Solution. We can
To complete this database, you will need the following file:
= CHAPTER 6 Access More Skills 11 Add Option Groups to Forms An option group is a frame with a set of check boxes, toggle buttons, or option buttons. Option groups can be bound or unbound to a field. When
Exploring Rational Functions
Name Date Period Exploring Rational Functions Part I - The numerator is a constant and the denominator is a linear factor. 1. The parent function for rational functions is: Graph and analyze this function:
3.5. Rational Functions: Graphs, Applications, and Models
3.5 Rational Functions: s, Applications, and Models The Reciprocal Function The Function Asympototes Steps for ing Rational Functions Rational Function Models Copyright 2008 Pearson Addison-Wesley. All
Lesson 5.2: Transformations of Sinusoidal Functions (Sine and Cosine)
Lesson 5.2: Transformations of Sinusoidal Functions (Sine and Cosine) Reflections Horizontal Translation (c) Vertical Translation (d) Remember: vertical stretch horizontal stretch 1 Part A: Reflections
Quadratics and their Properties
Algebra 2 Quadratics and their Properties Name: Ms. Williams/Algebra 2 Pd: 1 Table of Contents Day 1: COMPLETING THE SQUARE AND SHIFTING PARABOLAS SWBAT: Write a quadratic from standard form to vertex
Solve the following system of equations. " 2x + 4y = 8 # $ x 3y = 1. 1 cont d. You try:
1 Solve the following system of equations. " 2x + 4y = 8 # $ x 3y = 1 Method 1: Substitution 1. Solve for x in the second equation. 1 cont d Method 3: Eliminate y 1. Multiply first equation by 3 and second
2. Graphical Transformations of Functions
2. Graphical Transformations of Functions In this section we will discuss how the graph of a function may be transformed either by shifting, stretching or compressing, or reflection. In this section let
Acc. Pre Calculus Day 5 - Parabolas Notesheet PARABOLAS
Acc. Pre Calculus Day 5 - Parabolas Notesheet Name Date Block 1) Complete these truths about parabolas: * Parabolas are - shaped. PARABOLAS * Parabolas have a line of. * Parabolas are the graphs of functions.
Precalculus Chapter 2A Practice Guide Name
Precalculus Chapter A Practice Guide Name Day 1 Day.1 (page 96). (page 108 ).3 (page 1) 15,1,,3,7,33 37,4,49,50,5,55 17,30,38,47,53,61 67,85 Day 3 43,48,51,68 1,4,6,7,13,16,18,19.4 Worksheets.5 (page 145)
Algebra II Notes Transformations Unit 1.1. Math Background
Lesson. - Parent Functions and Transformations Math Background Previously, you Studied linear, absolute value, exponential and quadratic equations Graphed linear, absolute value, exponential and quadratic
LESSON 6 ADD A GRAPH TO A QUESTION
LESSON 6 ADD A GRAPH TO A QUESTION The next four lessons will focus on the different math objects you can add to your custom question. These objects include graphs, number lines, figures, pie charts, and
GUIDED NOTES 3.5 TRANSFORMATIONS OF FUNCTIONS
GUIDED NOTES 3.5 TRANSFORMATIONS OF FUNCTIONS LEARNING OBJECTIVES In this section, you will: Graph functions using vertical and horizontal shifts. Graph functions using reflections about the x-axis and
MHF4U. Advanced Functions Grade 12 University Mitchell District High School. Unit 5 Trig Functions & Equations 5 Video Lessons
MHF4U Advanced Functions Grade 12 University Mitchell District High School Unit 5 Trig Functions & Equations 5 Video Lessons Allow no more than 12 class days for this unit! This includes time for review
Student Exploration: Translating and Scaling Functions
Name: Date: Student Exploration: Translating and Scaling Functions Vocabulary: amplitude, parent function, periodic function, scale (a function), transform (a function), translate (a function) Prior Knowledge
Properties of a Function s Graph
Section 3.2 Properties of a Function s Graph Objective 1: Determining the Intercepts of a Function An intercept of a function is a point on the graph of a function where the graph either crosses or touches
February 14, S2.5q Transformations. Vertical Stretching and Shrinking. Examples. Sep 19 3:27 PM. Sep 19 3:27 PM.
MAT 171 Precalculus Algebra Dr. Claude Moore Cape Fear Community College CHAPTER 2: More on Functions 2.1 Increasing, Decreasing, and Piecewise Functions; Applications 2.2 The Algebra of Functions 2.3
Functions and Families
Unit 3 Functions and Families Name: Date: Hour: Function Transformations Notes PART 1 By the end of this lesson, you will be able to Describe horizontal translations and vertical stretches/shrinks of functions
Algebra 2 Graphing Project. 1. You must create a picture or artistic design using the graphs of at least 10 different functions and relations.
Algebra 2 Graphing Project Directions: 1. You must create a picture or artistic design using the graphs of at least 10 different functions and relations. 2. Your picture must include at least one of each
Microsoft Excel Using Excel in the Science Classroom
Microsoft Excel Using Excel in the Science Classroom OBJECTIVE Students will take data and use an Excel spreadsheet to manipulate the information. This will include creating graphs, manipulating data,
Name Course Days/Start Time
Name Course Days/Start Time Mini-Project : The Library of Functions In your previous math class, you learned to graph equations containing two variables by finding and plotting points. In this class, we
A function: A mathematical relationship between two variables (x and y), where every input value (usually x) has one output value (usually y)
SESSION 9: FUNCTIONS KEY CONCEPTS: Definitions & Terminology Graphs of Functions - Straight line - Parabola - Hyperbola - Exponential Sketching graphs Finding Equations Combinations of graphs TERMINOLOGY
Determine if the lines defined by the given equations are parallel, perpendicular, or neither. 1) -4y = 2x + 5
Review test 3 -College Algebra Math1314 - Spring 2017 - Houston Community College Name Date MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Determine
Algebra I Notes Absolute Value Functions Unit 04c
OBJECTIVES: F.IF.B.4 Interpret functions that arise in applications in terms of the context. For a function that models a relationship between two quantities, interpret key features of graphs and tables
Unit 2 Day 11. Quadratic Inequalities & Systems
Unit Day 11 Quadratic Inequalities & Systems 1 Warm Up 1. Given the following functions, specifically describe the transformation from the identity function y = x a. y = (x+3) 7 b. y = 5x + 1 c. y = ½(x
Section 4.3. Graphing Exponential Functions
Graphing Exponential Functions Graphing Exponential Functions with b > 1 Graph f x = ( ) 2 x Graphing Exponential Functions by hand. List input output pairs (see table) Input increases by 1 and output
Lesson 20: Four Interesting Transformations of Functions
Student Outcomes Students apply their understanding of transformations of functions and their graphs to piecewise functions. Lesson Notes In Lessons 17 19 students study translations and scalings of functions
Geometry Pre AP Graphing Linear Equations
Geometry Pre AP Graphing Linear Equations Name Date Period Find the x- and y-intercepts and slope of each equation. 1. y = -x 2. x + 3y = 6 3. x = 2 4. y = 0 5. y = 2x - 9 6. 18x 42 y = 210 Graph each
Geometry: Angle Relationships
Geometry: Angle Relationships I. Define the following angles (in degrees) and draw an example of each. 1. Acute 3. Right 2. Obtuse 4. Straight Complementary angles: Supplementary angles: a + b = c + d
Complex Numbers, Polar Equations, and Parametric Equations. Copyright 2017, 2013, 2009 Pearson Education, Inc.
8 Complex Numbers, Polar Equations, and Parametric Equations Copyright 2017, 2013, 2009 Pearson Education, Inc. 1 8.5 Polar Equations and Graphs Polar Coordinate System Graphs of Polar Equations Conversion
FUNCTIONS AND MODELS
1 FUNCTIONS AND MODELS FUNCTIONS AND MODELS 1.3 New Functions from Old Functions In this section, we will learn: How to obtain new functions from old functions and how to combine pairs of functions. NEW