Introduction to Parent Functions

Slides:



Advertisements
Similar presentations
Using Transformations to Graph Quadratic Functions 5-1
Advertisements

Using Transformations to Graph Quadratic Functions 5-1
Introduction to Parent Functions
Parent Function Transformation Students will be able to find determine the parent function or the transformed function given a function or graph.
Teaching note: after Bell Ringer Start with video: Lesson 1-2, part 1 Lesson Tutorial Video (blue); -tell students when watching video: just listen, we.
Warm Up Use the graph for Problems 1–2.
Exponential Functions
Objective Transform polynomial functions..
Introduction to Parent Functions
In Chapters 2 and 3, you studied linear functions of the form f(x) = mx + b. A quadratic function is a function that can be written in the form of f(x)
Radical Functions Warm Up Lesson Presentation Lesson Quiz
Warm Up For each translation of the point (–2, 5), give the coordinates of the translated point units down (–2, –1) 2. 3 units right (1, 5) For each.
6-8 Transforming Polynomial Functions Warm Up Lesson Presentation
Transform quadratic functions.
Radical Functions 8-7 Warm Up Lesson Presentation Lesson Quiz
Warm Up Identify the domain and range of each function.
2.2 b Writing equations in vertex form
Chapter 1 - Foundations for Functions
Objectives Graph radical functions and inequalities.
An absolute-value function is a function whose rule contains an absolute-value expression. The graph of the parent absolute-value function f(x) = |x| has.
Holt McDougal Algebra Exponential Functions 9-2 Exponential Functions Holt Algebra 1 Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson.
Holt McDougal Algebra Introduction to Parent Functions 1-2 Introduction to Parent Functions Holt Algebra 2 Warm Up Warm Up Lesson Presentation Lesson.
Absolute–Value Functions
Chapter 1 -Foundations for Functions
Foundations for Functions Chapter Exploring Functions Terms you need to know – Transformation, Translation, Reflection, Stretch, and Compression.
Similar to the way that numbers are classified into sets based on common characteristics, functions can be classified into families of functions. The parent.
M3U6D1 Warm Up Identify the domain and range of each function. D: R ; R:{y|y ≥2} 1. f(x) = x D: R ; R: R 2. f(x) = 3x 3 Use the description to write.
Holt McDougal Algebra Using Transformations to Graph Quadratic Functions Warm Up For each translation of the point (–2, 5), give the coordinates.
How does each function compare to its parent function?
Warm Up Give the coordinates of each transformation of (2, –3). 4. reflection across the y-axis (–2, –3) 5. f(x) = 3(x + 5) – 1 6. f(x) = x 2 + 4x Evaluate.
Holt McDougal Algebra 2 Radical Functions Graph radical functions and inequalities. Transform radical functions by changing parameters. Objectives.
Objectives Transform quadratic functions.
Holt Algebra Linear, Quadratic, and Exponential Models Warm Up Find the slope and y-intercept of the line that passes through (4, 20) and (20, 24).
*Review Lesson 6.1, 6.2 & 6.3: Understanding, Graphing, Transforming Quadratic Functions (Pgs )
Exponential Functions
Introduction to Parent Functions
Warm Up For each translation of the point (–2, 5), give the coordinates of the translated point units down 2. 3 units right For each function, evaluate.
Find the x and y intercepts.
Introduction to Parent Functions
13 Algebra 1 NOTES Unit 13.
Using Transformations to Graph Quadratic Functions 5-1
6-8 Transforming Polynomial Functions Warm Up Lesson Presentation
2.6 Translations and Families of Functions
Exponential Functions
6-8 Transforming Polynomial Functions Warm Up Lesson Presentation
Exponential Functions
Objectives Transform quadratic functions.
Exponential Functions
Introduction to Parent Functions
4-2 Using Intercepts Warm Up Lesson Presentation Lesson Quiz
Exploring Transformations
Objectives Transform quadratic functions.
3-8 Transforming Polynomial Functions Warm Up Lesson Presentation
29/01/2013 Systems of Inequalities Chapter 3.2 PAGE
Introduction to Conic Sections
Introduction to Parent Functions
Objectives Identify parent functions from graphs and equations.
Parent Functions.
Parent Functions.
Objective Transform polynomial functions..
P A R B O L S.
Transforming Linear Functions
Introduction to Parent Functions
Introduction to Parent Functions
Objectives Identify parent functions from graphs and equations.
Absolute–Value Functions
Exponential Functions
Exponential Functions
Exponential Functions
Presentation transcript:

Introduction to Parent Functions 1-2 Introduction to Parent Functions Warm Up Lesson Presentation Lesson Quiz Holt McDougal Algebra 2 Holt Algebra 2

Warm Up 1. For the power 35, identify the exponent and the base. Evaluate. 2. 3. f(9) when f(x)=2x + exponent: 5; base: 3 21

Objectives Identify parent functions from graphs and equations. Use parent functions to model real-world data and make estimates for unknown values.

Vocabulary parent function

Similar to the way that numbers are classified into sets based on common characteristics, functions can be classified into families of functions. The parent function is the simplest function with the defining characteristics of the family. Functions in the same family are transformations of their parent function.

Parent Functions

To make graphs appear accurate on a graphing calculator, use the standard square window. Press ZOOM , choose 6:ZStandard, press again, and choose 5:ZSquare. Helpful Hint ZOOM ZOOM

Example 1A: Identifying Transformations of Parent Functions Identify the parent function for g from its function rule. Then graph g on your calculator and describe what transformation of the parent function it represents. g(x) = x – 3 g(x) = x – 3 is linear x has a power of 1. The linear parent function ƒ(x) = x intersects the y-axis at the point (0, 0). Graph Y1 = x – 3 on the graphing calculator. The function g(x) = x – 3 intersects the y-axis at the point (0, –3). So g(x) = x – 3 represents a vertical translation of the linear parent function 3 units down.

Example 1B: Identifying Transformations of Parent Functions Identify the parent function for g from its function rule. Then graph on your calculator and describe what transformation of the parent function it represents. g(x) = x2 + 5 g(x) = x2 + 5 is quadratic. x has a power of 2. The quadratic parent function ƒ(x) = x2 intersects the y-axis at the point (0, 0). Graph Y1 = x2 + 5 on a graphing calculator. The function g(x) = x2 + 5 intersects the y-axis at the point (0, 5). So g(x) = x2 + 5 represents a vertical translation of the quadratic parent function 5 units up.

Check It Out! Example 1a g(x) = x3 + 2 g(x) = x3 + 2 is cubic. Identify the parent function for g from its function rule. Then graph on your calculator and describe what transformation of the parent function it represents. g(x) = x3 + 2 g(x) = x3 + 2 is cubic. x has a power of 3. The cubic parent function ƒ(x) = x3 intersects the y-axis at the point (0, 0). Graph Y1 = x3 + 2 on a graphing calculator. The function g(x) = x3 + 2 intersects the y-axis at the point (0, 2). So g(x) = x3 + 2 represents a vertical translation of the cubic parent function 2 units up.

g(x) = (–x)2 is quadratic. x has a power of 2. Check It Out! Example 1b Identify the parent function for g from its function rule. Then graph on your calculator and describe what transformation of the parent function it represents. g(x) = (–x)2 g(x) = (–x)2 is quadratic. x has a power of 2. The quadratic parent function ƒ(x) = x2 intersects the y-axis at the point (0, 0). Graph Y1 = (–x)2 on a graphing calculator. The function g(x) = (–x)2 intersects the y-axis at the point (0, 0). So g(x) = (–x)2 represents a reflection across the y-axis of the quadratic parent function.

It is often necessary to work with a set of data points like the ones represented by the table below. x –4 –2 2 4 y 8 With only the information in the table, it is impossible to know the exact behavior of the data between and beyond the given points. However, a working knowledge of the parent functions can allow you to sketch a curve to approximate those values not found in the table.

Example 2: Identifying Parent Functions to Model Data Sets Graph the data from this set of ordered pairs. Describe the parent function and the transformation that best approximates the data set. {(–2, 12), (–1, 3), (0, 0), (1, 3), (2, 12)} x –2 –1 1 2 y 12 3 The graph of the data points resembles the shape of the quadratic parent function ƒ(x) = x2. The quadratic parent function passes through the points (1, 1) and (2, 4). The data set contains the points (1, 1) = (1, 3(1)) and (2, 4) = (2, 3(4)). The data set seems to represent a vertical stretch of the quadratic parent function by a factor of 3.

x –4 –2 2 4 y –12 –6 6 12 Check It Out! Example 2      Graph the data from the table. Describe the parent function and the transformation that best approximates the data set.  x –4 –2 2 4 y –12 –6 6 12  The graph of the data points resembles the shape of the linear parent function ƒ(x) = x.  The linear parent function passes through the points (2, 2) and (4, 4). The data set contains the points (2, 2) = (2, 3(2)) and (4, 4) = (4, 3(4)).   The data set seems to represent a vertical stretch of the linear function by a factor of 3.

Consider the two data points (0, 0) and (0, 1) Consider the two data points (0, 0) and (0, 1). If you plot them on a coordinate plane you might very well think that they are part of a linear function. In fact they belong to each of the parent functions below. Remember that any parent function you use to approximate a set of data should never be considered exact. However, these function approximations are often useful for estimating unknown values.

Example 3: Application Graph the relationship from year to sales in millions of dollars and identify which parent function best describes it. Then use the graph to estimate when cumulative sales reached $10 million. 12.6 5 7.8 4 4.2 3 1.8 2 0.6 1 Sales (million $) Year Cumulative Sales Step 1 Graph the relation. Graph the points given in the table. Draw a smooth curve through them to help you see the shape.

Example 3 Continued Step 2 Identify the parent function. The graph of the data set resembles the shape of the quadratic parent function f(x) = x2. Step 3 Estimate when cumulative sales reached $10 million. The curve indicates that sales will reach the $10 million mark after about 4.5 years.

Check It Out! Example 3 The cost of playing an online video game depends on the number of months for which the online service is used. Graph the relationship from number of months to cost, and identify which parent function best describes the data. Then use the graph to estimate the cost of 5 months of online service.

Check It Out! Example 3 Continued Step 1 Graph the relation. Graph the points given in the table. Draw a smooth line through them to help you see the shape. Step 2 Identify the parent function. The graph of the data set resembles the shape of a linear parent function ƒ(x) = x. Step 3 Estimate the cost for 5 months of online service. The linear graph indicates that the cost for 5 months of online service is $72.

Lesson Quiz: Part I Identify the parent function for g from its function rule. Then graph g on your calculator and describe what transformation of the parent function it represents. 1. g(x) = x + 7 linear; translation up 7 units

Lesson Quiz: Part II Identify the parent function for g from its function rule. Then graph g on your calculator and describe what transformation of the parent function it represents. 2. g(x) = x2 – 7 quadratic; translation down 6 units

linear: 8 hr Lesson Quiz: Part III 3. Stacy earns $7.50 per hour. Graph the relationship from hours to amount earned and identify which parent function best describes it. Then use the graph to estimate how many hours it would take Stacy to earn $60. linear: 8 hr