Lesson #1: Exponential Functions and Their Inverses Day 2
|
|
|
- Octavia Regina Phillips
- 6 years ago
- Views:
Transcription
1 Unit 5: Logarithmic Functions Lesson #1: Exponential Functions and Their Inverses Day 2 Exponential Functions & Their Inverses Exponential Functions are in the form. The inverse of an exponential is a reflection in the line. The and coordinates are swapped. Inverse of the exponential function : Solve for : log Unit 8 1
2 Properties of a Logarithmic Function The domain is all positive real numbers 0or 0,. The range is all real numbers,,. The vertical asymptote is located at 0 (the -axis). The intercept is (1,0). Example 1: Graph of 2. Unit 8 2
3 Transformations of Logarithmic Functions Using HSRV Logarithmic Functions and Reflections Recall, when reflecting over the axis, the value is negated. The vertical asymptote remains at 0. Unit 8 3
4 Logarithmic Functions and Reflections Recall, when reflecting over the axis, the value is negated. The vertical asymptote remains at 0. Logarithmic Functions and Translations If h is positive, the graph shifts to the right units. (Remember: if h looks negative h is positive) If h is negative, the graph shifts to the left units. (Remember: if h looks positive h is negative) The line is the vertical asymptote. The domain is. The range is, or all real numbers. Unit 8 4
5 Logarithmic Functions and Translations If is positive, the graph shifts up units. If is negative, the graph shifts down units. If 1, the graph moves up to the right,. If 0 1 the graph moves down to the right. Logarithmic Functions: Stretch & Shrink If 1, multiply each coordinate of by, vertically stretching the graph of by the factor of. If 0 1, multiply each coordinate of by, vertically shrinking the graph of by the factor of. If 1, divide each coordinate of by, horizontally shrinking the graph of by the factor of. If 0 1, divide each coordinate of by, horizontally stretching the graph of by the factor of. Unit 8 5
6 Transformations of Functions Recall: Combinations of Transformations: A function involving more than one transformation can be graphed by performing transformations in the following order: 1. Horizontal Shifting 2. Stretching or Shrinking 3. Reflecting 4. Vertical Shifting Ex 1: Describe the graph of 2log 1. Transformation: H none S vertical stretch by factor of 2 (multiply s by 2) R reflect over the axis V up 1 Domain: or, Range:, Asymptote: Unit 8 6
7 Ex 2: Describe the graph of log Transformation: H left 3 S horizontal shrink by factor of 2 (divide s by 2) R none V down 4 Domain: or, Range:, Asymptote: Ex 3: Use the graph of log and transformations to sketch the graph of log 1 4. Also, find the domain and vertical asymptote of. H left 1 unit S none R none V up 4 units Domain:, Unit 8 7
8 Ex 4: Use the graph of log and transformations to sketch the graph of 2log 4 1. Also, find the domain & vertical asymptote of. H left 4 units S vertical stretch by factor (multiply values by ) R none V down 1 unit Domain:, Ex 5: Use the graph of log and transformations to sketch the graph of log 5 4. Also, find the domain & vertical asymptote of. H left 5 units S horizontal stretch by factor (divide values by ) R reflection over axis (negate values) V down 4 units Domain:, Unit 8 8
9 Ex 6: Determine the domain and vertical asymptote of the graph of log Recall: Domain of a logarithmic function is all real numbers greater than zero. Domain:, Ex 7: Determine the domain and vertical asymptote of the graph of log Domain:, Unit 8 9
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
Graphs of Increasing Exponential Functions
Section 5 2A: Graphs of Increasing Exponential Functions We want to determine what the graph of an exponential function y = a x looks like for all values of a > We will select a value of a > and examine
Graphs of Increasing Exponential Functions
Section 5 2A: Graphs of Increasing Exponential Functions We want to determine what the graph of an exponential function y = a x looks like for all values of a > We will select a value of a > and examine
We want to determine what the graph of an exponential function y = a x looks like for all values of a such that 0 < a < 1
Section 5 2B: Graphs of Decreasing Eponential Functions We want to determine what the graph of an eponential function y = a looks like for all values of a such that 0 < a < We will select a value of a
Translation of graphs (2) The exponential function and trigonometric function
Lesson 35 Translation of graphs (2) The exponential function and trigonometric function Learning Outcomes and Assessment Standards Learning Outcome 2: Functions and Algebra Assessment Standard Generate
WARM UP DESCRIBE THE TRANSFORMATION FROM F(X) TO G(X)
WARM UP DESCRIBE THE TRANSFORMATION FROM F(X) TO G(X) 2 5 5 2 2 2 2 WHAT YOU WILL LEARN HOW TO GRAPH THE PARENT FUNCTIONS OF VARIOUS FUNCTIONS. HOW TO IDENTIFY THE KEY FEATURES OF FUNCTIONS. HOW TO TRANSFORM
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
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
Skills Practice Skills Practice for Lesson 7.1
Skills Practice Skills Practice for Lesson.1 Name Date What s the Inverse of an Eponent? Logarithmic Functions as Inverses Vocabulary Write the term that best completes each statement. 1. The of a number
Graphs of Exponential
Graphs of Exponential Functions By: OpenStaxCollege As we discussed in the previous section, exponential functions are used for many realworld applications such as finance, forensics, computer science,
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 4.2 Graphs of Exponential Functions
238 Chapter 4 Section 4.2 Graphs of Eponential Functions Like with linear functions, the graph of an eponential function is determined by the values for the parameters in the function s formula. To get
Unit 3: Absolute Value
Name: Block: Unit 3: Absolute Value Day 1: Characteristics of Absolute Value Day 2: Transformations of Absolute Value Day 3: Absolute Value Equations Day 4: Absolute Value Inequalities 1 DAY1: The Absolute
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
Radical Functions. Attendance Problems. Identify the domain and range of each function.
Page 1 of 12 Radical Functions Attendance Problems. Identify the domain and range of each function. 1. f ( x) = x 2 + 2 2. f ( x) = 3x 3 Use the description to write the quadratic function g based on the
Check In before class starts:
Name: Date: Lesson 5-3: Graphing Trigonometric Functions Learning Goal: How do I use the critical values of the Sine and Cosine curve to graph vertical shift and vertical stretch? Check In before class
Start Fred Functions. Quadratic&Absolute Value Transformations. Graphing Piecewise Functions Intro. Graphing Piecewise Practice & Review
Honors CCM2 Unit 6 Name: Graphing Advanced Functions This unit will get into the graphs of simple rational (inverse variation), radical (square and cube root), piecewise, step, and absolute value functions.
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) =
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
CHAPTER 5: Exponential and Logarithmic Functions
MAT 171 Precalculus Algebra Dr. Claude Moore Cape Fear Community College CHAPTER 5: Exponential and Logarithmic Functions 5.1 Inverse Functions 5.2 Exponential Functions and Graphs 5.3 Logarithmic Functions
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
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
Exponential and Logarithmic Functions. College Algebra
Exponential and Logarithmic Functions College Algebra Exponential Functions Suppose you inherit $10,000. You decide to invest in in an account paying 3% interest compounded continuously. How can you calculate
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
Objectives Graph and Analyze Rational Functions Find the Domain, Asymptotes, Holes, and Intercepts of a Rational Function
SECTIONS 3.5: Rational Functions Objectives Graph and Analyze Rational Functions Find the Domain, Asymptotes, Holes, and Intercepts of a Rational Function I. Rational Functions A rational function is a
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
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
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
Name Homework Packet Week #12
1. All problems with answers or work are examples. Lesson 4.4 Complete the table for each given sequence then graph each sequence on the coordinate plane. Term Number (n) Value of Term ( ) 1 2 3 4 5 6
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:
GRAPHING CALCULATOR - WINDOW SIZING
Section 1.1 GRAPHING CALCULATOR - WINDOW SIZING WINDOW BUTTON. Xmin= Xmax= Xscl= Ymin= Ymax= Yscl= Xres=resolution, smaller number= clearer graph Larger number=quicker graphing Xscl=5, Yscal=1 Xscl=10,
Pure Math 30: Explained!
www.puremath30.com 30 part i: stretches about other lines Stretches about other lines: Stretches about lines other than the x & y axis are frequently required. Example 1: Stretch the graph horizontally
2/22/ Transformations but first 1.3 Recap. Section Objectives: Students will know how to analyze graphs of functions.
1 2 3 4 1.4 Transformations but first 1.3 Recap Section Objectives: Students will know how to analyze graphs of functions. 5 Recap of Important information 1.2 Functions and their Graphs Vertical line
Section Graphs of the Sine and Cosine Functions
Section 5. - Graphs of the Sine and Cosine Functions In this section, we will graph the basic sine function and the basic cosine function and then graph other sine and cosine functions using transformations.
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
1.1 Pearson Modeling and Equation Solving
Date:. Pearson Modeling and Equation Solving Syllabus Objective:. The student will solve problems using the algebra of functions. Modeling a Function: Numerical (data table) Algebraic (equation) Graphical
Rational functions, like rational numbers, will involve a fraction. We will discuss rational functions in the form:
Name: Date: Period: Chapter 2: Polynomial and Rational Functions Topic 6: Rational Functions & Their Graphs Rational functions, like rational numbers, will involve a fraction. We will discuss rational
Transformations of Exponential Functions
7-2 Transformations of Exponential Functions PearsonTEXAS.com SOLVE IT! f and g are exponential functions with the same base. Is the graph of g a compression, a reflection, or a translation of the graph
Section 2.3 (e-book 4.1 & 4.2) Rational Functions
Section 2.3 (e-book 4.1 & 4.2) Rational Functions Definition 1: The ratio of two polynomials is called a rational function, i.e., a rational function has the form, where both and are polynomials. Remark
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
3.7 Rational Functions. Copyright Cengage Learning. All rights reserved.
3.7 Rational Functions Copyright Cengage Learning. All rights reserved. Objectives Rational Functions and Asymptotes Transformations of y = 1/x Asymptotes of Rational Functions Graphing Rational Functions
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
2-3 Graphing Rational Functions
2-3 Graphing Rational Functions Factor What are the end behaviors of the Graph? Sketch a graph How to identify the intercepts, asymptotes and end behavior of a rational function. How to sketch the graph
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
Chapter 2(part 2) Transformations
Chapter 2(part 2) Transformations Lesson Package MCR3U 1 Table of Contents Lesson 1: Intro to transformations.... pg. 3-7 Lesson 2: Transformations of f x = x!...pg. 8-11 Lesson 3: Transformations of f
2-4 Graphing Rational Functions
2-4 Graphing Rational Functions Factor What are the zeros? What are the end behaviors? How to identify the intercepts, asymptotes, and end behavior of a rational function. How to sketch the graph of a
CURVE SKETCHING EXAM QUESTIONS
CURVE SKETCHING EXAM QUESTIONS Question 1 (**) a) Express f ( x ) in the form ( ) 2 f x = x + 6x + 10, x R. f ( x) = ( x + a) 2 + b, where a and b are integers. b) Describe geometrically the transformations
Transformation of curve. a. reflect the portion of the curve that is below the x-axis about the x-axis
Given graph of y f = and sketch:. Linear Transformation cf ( b + a) + d a. translate a along the -ais. f b. scale b along the -ais c. scale c along the y-ais d. translate d along the y-ais Transformation
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
Graphing Radical Functions
17 LESSON Graphing Radical Functions Basic Graphs of Radical Functions UNDERSTAND The parent radical function, 5, is shown. 5 0 0 1 1 9 0 10 The function takes the principal, or positive, square root of.
Mastery. PRECALCULUS Student Learning Targets
PRECALCULUS Student Learning Targets Big Idea: Sequences and Series 1. I can describe a sequence as a function where the domain is the set of natural numbers. Connections (Pictures, Vocabulary, Definitions,
Reminder: y =f(x) mean that a function f uses a variable (an ingredient) x to make the result y.
Functions (.3) Reminder: y =f(x) mean that a function f uses a variable (an ingredient) x to make the result y.. Transformation of functions 3 We know many elementary functions like f ( x) = x + x + 3x+,
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
State the domain and range of the relation shown in the graph. Is the relation a function? You try: A relation is represented by
1 State the domain and range of the relation shown in the graph. Is the relation a function? 1a A relation is represented by! Remember: A relation is a set of ordered pairs that can be represented by a
Exploring Quadratic Graphs
Exploring Quadratic Graphs The general quadratic function is y=ax 2 +bx+c It has one of two basic graphs shapes, as shown below: It is a symmetrical "U"-shape or "hump"-shape, depending on the sign of
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
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
8.6. Write and Graph Exponential Decay Functions. Warm Up Lesson Presentation Lesson Quiz
8.6 Write and Graph Exponential Decay Functions Warm Up Lesson Presentation Lesson Quiz 8.6 Warm-Up. Evaluate. 3 ANSWER 8. Evaluate. 4 ANSWER 6 3. The table shows how much money Tess owes after w weeks.
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 - - - - - - - -
IB Math SL Year 2 Name: Date: 2-1: Laws of Exponents, Equations with Exponents, Exponential Function
Name: Date: 2-1: Laws of Exponents, Equations with Exponents, Exponential Function Key Notes What do I need to know? Notes to Self 1. Laws of Exponents Definitions for: o Exponent o Power o Base o Radical
Graphing Techniques. Domain (, ) Range (, ) Squaring Function f(x) = x 2 Domain (, ) Range [, ) f( x) = x 2
Graphing Techniques In this chapter, we will take our knowledge of graphs of basic functions and expand our ability to graph polynomial and rational functions using common sense, zeros, y-intercepts, stretching
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
College Algebra. Fifth Edition. James Stewart Lothar Redlin Saleem Watson
College Algebra Fifth Edition James Stewart Lothar Redlin Saleem Watson 4 Polynomial and Rational Functions 4.6 Rational Functions Rational Functions A rational function is a function of the form Px (
THE RECIPROCAL FUNCTION FAMILY AND RATIONAL FUNCTIONS AND THEIR GRAPHS L E S S O N 9-2 A N D L E S S O N 9-3
THE RECIPROCAL FUNCTION FAMILY AND RATIONAL FUNCTIONS AND THEIR GRAPHS L E S S O N 9-2 A N D L E S S O N 9-3 ASSIGNMENT 2/12/15 Section 9-2 (p506) 2, 6, 16, 22, 24, 28, 30, 32 section 9-3 (p513) 1 18 Functions
Core Mathematics 3 Functions
http://kumarmaths.weebly.com/ Core Mathematics 3 Functions Core Maths 3 Functions Page 1 Functions C3 The specifications suggest that you should be able to do the following: Understand the definition of
0,0 is referred to as the end point.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 Chapter 2: Radical Functions 2.1 Radical Functions and Transformations (Day 1) For the function y x, the radicand, x, must
Lesson 20: Every Line is a Graph of a Linear Equation
Student Outcomes Students know that any non vertical line is the graph of a linear equation in the form of, where is a constant. Students write the equation that represents the graph of a line. Lesson
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
3.5D Graphing Rational Functions
3.5D Graphing Rational Functions A. Strategy 1. Find all asymptotes (vertical, horizontal, oblique, curvilinear) and holes for the function. 2. Find the and intercepts. 3. Plot the and intercepts, draw
Radical and Rational Function Exam Questions
Radical and Rational Function Exam Questions Name: ANSWERS 2 Multiple Choice 1. Identify the graph of the function x y. x 2. Given the graph of y f x, what is the domain of x f? a. x R b. 2 x 2 c. x 2
Name: Teacher: Pd: Algebra 2/Trig: Trigonometric Graphs (SHORT VERSION)
Algebra 2/Trig: Trigonometric Graphs (SHORT VERSION) In this unit, we will Learn the properties of sine and cosine curves: amplitude, frequency, period, and midline. Determine what the parameters a, b,
Investigating Transformations With DESMOS
MPM D0 Date: Investigating Transformations With DESMOS INVESTIGATION Part A: What if we add a constant to the x in y = x? 1. Use DESMOS to graph the following quadratic functions on the same grid. Graph
Unit 4: Radicals and Rationals. Shreya Nadendla, Sahana Devaraj, Divya Hebbar
Unit 4: Radicals and Rationals Shreya Nadendla, Sahana Devaraj, Divya Hebbar What is a RATIONAL function? A rational function is any function which can be defined by a rational fraction. It is an algebraic
Walt Whitman High School SUMMER REVIEW PACKET. For students entering AP CALCULUS BC
Walt Whitman High School SUMMER REVIEW PACKET For students entering AP CALCULUS BC Name: 1. This packet is to be handed in to your Calculus teacher on the first day of the school year.. All work must be
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
Pre-Calculus Summer Assignment
Pre-Calculus Summer Assignment Identify the vertex and the axis of symmetry of the parabola. Identify points corresponding to P and Q. 1. 2. Find a quadratic model for the set of values. 3. x 2 0 4 f(x)
Section 2.2 Graphs of Linear Functions
Section. Graphs of Linear Functions Section. Graphs of Linear Functions When we are working with a new function, it is useful to know as much as we can about the function: its graph, where the function
Lesson 19: Four Interesting Transformations of Functions
Student Outcomes Students examine that a horizontal scaling with scale factor of the graph of corresponds to changing the equation from to 1. Lesson Notes In this lesson, students study the effect a horizontal
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
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)
Unit 5: Quadratic Functions
Unit 5: Quadratic Functions LESSON #5: THE PARABOLA GEOMETRIC DEFINITION DIRECTRIX FOCUS LATUS RECTUM Geometric Definition of a Parabola Quadratic Functions Geometrically, a parabola is the set of all
Math 083 Final Exam Practice
Math 083 Final Exam Practice Name: 1. Simplify the expression. Remember, negative exponents give reciprocals.. Combine the expressions. 3. Write the expression in simplified form. (Assume the variables
AP Calculus Summer Review Packet
AP Calculus Summer Review Packet Name: Date began: Completed: **A Formula Sheet has been stapled to the back for your convenience!** Email anytime with questions: danna.seigle@henry.k1.ga.us Complex Fractions
Pre-Calculus Mr. Davis
Pre-Calculus 2016-2017 Mr. Davis How to use a Graphing Calculator Applications: 1. Graphing functions 2. Analyzing a function 3. Finding zeroes (or roots) 4. Regression analysis programs 5. Storing values
Radical Functions Review
Radical Functions Review Specific Outcome 3 Graph and analyze radical functions (limited to functions involving one radical) Acceptable Standard sketch and analyze (domain, range, invariant points, - and
Section 7.6 Graphs of the Sine and Cosine Functions
Section 7.6 Graphs of the Sine and Cosine Functions We are going to learn how to graph the sine and cosine functions on the xy-plane. Just like with any other function, it is easy to do by plotting points.
Math 2 Spring Unit 5 Bundle Transformational Graphing and Inverse Variation
Math 2 Spring 2017 Unit 5 Bundle Transformational Graphing and Inverse Variation 1 Contents Transformations of Functions Day 1... 3 Transformations with Functions Day 1 HW... 10 Transformations with Functions
1 Review of Functions Symmetry of Functions; Even and Odd Combinations of Functions... 42
Contents 0.1 Basic Facts...................................... 8 0.2 Factoring Formulas.................................. 9 1 Review of Functions 15 1.1 Functions.......................................
,?...?, the? or? s are for any holes or vertical asymptotes.
Name: Period: Pre-Cal AB: Unit 14: Rational Functions Monday Tuesday Block Friday 16 17 18/19 0 end of 9 weeks Graphing Rational Graphing Rational Partial Fractions QUIZ 3 Conic Sections (ON Friday s Quiz)
Graphical Methods Booklet
Graphical Methods Booklet This document outlines the topic of work and the requirements of students working at New Zealand Curriculum level 7. Parabola, vertex form y = x 2 Vertex (0,0) Axis of symmetry
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
Omit Present Value on pages ; Example 7.
MAT 171 Precalculus Algebra Trigsted Pilot Test Dr. Claude Moore Cape Fear Community College CHAPTER 5: Exponential and Logarithmic Functions and Equations 5.1 Exponential Functions 5.2 The Natural Exponential
Voluntary State Curriculum Algebra II
Algebra II Goal 1: Integration into Broader Knowledge The student will develop, analyze, communicate, and apply models to real-world situations using the language of mathematics and appropriate technology.
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
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
Session 3. Rational and Radical Equations. Math 30-1 R 3. (Revisit, Review and Revive)
Session 3 Rational and Radical Equations Math 30-1 R 3 (Revisit, Review and Revive) Rational Functions Review Specific Outcome 14 Graph and analyze rational functions (limited to numerators and denominators
The Graph of an Equation Graph the following by using a table of values and plotting points.
Precalculus - Calculus Preparation - Section 1 Graphs and Models Success in math as well as Calculus is to use a multiple perspective -- graphical, analytical, and numerical. Thanks to Rene Descartes we
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
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)
Goal: Graph rational expressions by hand and identify all important features
Goal: Graph rational expressions by hand and identify all important features Why are we doing this? Rational expressions can be used to model many things in our physical world. Understanding the features