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Name: ___________________________________ # ___________ Honors Coordinate Algebra: Period _____________ Ms. Pierre Date: ______________

3.7.2 Transformations of Linear and Exponential Functions

Warm Up

LINEAR AND EXPONENTIAL FUNCTIONSLesson 7: Operating on Functions and Transformations

NAME:

CCGPS Coordinate Algebra Teacher Resource Binder © Walch EducationU3-371

Lesson 3.7.2: Transformations of Linear and Exponential FunctionsWarm-Up 3.7.2On a map, Maple Street is represented by the function f(x) = 2x – 1, and Highland Street is represented by the function g(x) = 2x + 3. Graph both functions on the same set of axes.

1. How are the two graphs similar?

2. How are the two graphs different?

3. How could you describe the geometric translation from f(x) to g(x)?


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NAME:






Chant Lyrics:

In the class, in the class going up, down, Signs the same, + for up, - for down K’s on the street (x3) Outside parentheses In the class, in the class going left, right, Signs reverse, + for left, - for right K’s next to me (x3) Inside parentheses


NAME:







Instruction

CCGPS Coordinate Algebra Teacher Resource Binder U3-374

© Walch Education

Prerequisite Skills

This lesson requires the use of the following skills:

• graphing linear and exponential functions

• translating functions

• identifying y-intercepts of graphs of functions

IntroductionIt is important to understand the relationship between a function and the graph of a function. In this lesson, we will explore how a function and its graph change when a constant value is added to the function. When a constant value is added to a function, the graph undergoes a vertical shift. A vertical shift is a type of translation that moves the graph up or down depending on the value added to the function. A translation of a graph moves the graph either vertically, horizontally, or both, without changing its shape. A translation is sometimes called a slide. A translation is a specific type of transformation. A transformation moves a graph. Transformations can include reflections and rotations in addition to translations. We will also examine translations of graphs and determine how they are similar or different.

Key Concepts• Vertical translations can be performed on linear and exponential graphs using f(x) + k, where

k is the value of the vertical shift.

• A vertical shift moves the graph up or down k units.

• If k is positive, the graph is translated up k units.

• If k is negative, the graph is translated down k units.

• Translations are one type of transformation.

• Given the graphs of two functions that are vertical translations of each other, the value of the vertical shift, k, can be found by finding the distance between the y-intercepts.

Common Errors/Misconceptions

• mistaking vertical shift for horizontal shift

• mistaking a y-intercept for the value of the vertical translation

• incorrectly graphing linear or exponential functions

• incorrectly combining like terms when changing a function rule

Example 1


Instruction


Guided Practice 3.7.2Example 1

Graph the following functions on the same set of axes:

f(x) = 3x

g(x) = 3x + 1

h(x) = 3x + 2

q(x) = 3x – 1

1. Graph the functions.

-3 -2 -1 0 1 2 3

-3

-2

-1

1

2

3

h(x) = 3x + 2q(x) = 3x – 1

g(x)

= 3x +

1f(x

) = 3x

2. What is the y-intercept of f(x)? g(x)? h(x)? q(x)?

The y-intercept of f(x) is 0.

The y-intercept of g(x) is 1.

The y-intercept of h(x) is 2.

The y-intercept of q(x) is –1.


Instruction




f(x) = 3x

g(x) = 3x + 1

h(x) = 3x + 2

q(x) = 3x – 1


-3 -2 -1 0 1 2 3

-3

-2

-1

1

2

3

h(x) = 3x + 2q(x) = 3x – 1

g(x)

= 3x +

1f(x

) = 3x







Instruction




f(x) = 3x

g(x) = 3x + 1

h(x) = 3x + 2

q(x) = 3x – 1


-3 -2 -1 0 1 2 3

-3

-2

-1

1

2

3

h(x) = 3x + 2q(x) = 3x – 1

g(x)

= 3x +

1f(x

) = 3x






Example 2


Instruction


© Walch Education

3. How could you describe the translation of h(x) from f(x)?

The graph of h(x) is shifted up 2 units from the graph of f(x).

4. How could you describe the translation of q(x) from f(x)?

The graph of q(x) is shifted down 1 unit from the graph of f(x).

5. How could you describe the translation of q(x) from g(x)?

The graph of q(x) is shifted down 2 units from the graph of g(x).

Example 2

Given f(x) = 2x + 1 and the graph of f(x) below, graph g(x) = f(x) – 5.

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f(x) = 2x + 1


Instruction


© Walch Education







Example 2


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f(x) = 2x + 1


Instruction


© Walch Education







Example 2


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f(x) = 2x + 1


Instruction


© Walch Education







Example 2


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f(x) = 2x + 1


Instruction


1. Graph g(x).

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f(x) = 2x + 1 g(x) = 2x – 4

2. How are f(x) and g(x) related?

g(x) is a vertical shift down 5 units of f(x).

3. What are the steps you need to follow to graph g(x)?

For each point on f(x), plot a point 5 units lower on the graph and connect the points.


Instruction


1. Graph g(x).

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f(x) = 2x + 1 g(x) = 2x – 4


g(x) is a vertical shift down 5 units of f(x).

3. What are the steps you need to follow to graph g(x)?

For each point on f(x), plot a point 5 units lower on the graph and connect the points.

Example 3


Instruction


© Walch Education

Example 3

The graphs of two functions f(x) and g(x) are shown below. Write a rule for g(x) in terms of f(x).

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10

f(x)

g(x)

1. Write a function rule for the graph of f(x).

f(x) = –x – 4

2. Write a function rule for the graph of g(x).

g(x) = –x + 3


g(x) is a vertical shift up 7 units from f(x), since the vertical distance is the distance between the y-intercepts (–4 and 3), and 3 – (–4) = 7. You could also count the units on the graph.

4. Write a function rule for g(x) in terms of f(x).

g(x) = f(x) + 7


Instruction


© Walch Education

Example 3


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10

f(x)

g(x)


f(x) = –x – 4


g(x) = –x + 3




g(x) = f(x) + 7


Instruction


© Walch Education

Example 3


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10

f(x)

g(x)


f(x) = –x – 4


g(x) = –x + 3




g(x) = f(x) + 7


Instruction


© Walch Education

Example 3


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10

f(x)

g(x)


f(x) = –x – 4


g(x) = –x + 3




g(x) = f(x) + 7


Instruction


© Walch Education

Example 3


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10

f(x)

g(x)


f(x) = –x – 4


g(x) = –x + 3




g(x) = f(x) + 7

Guided Practice

1. )


NAME:


© Walch Education

Practice 3.7.2: Transformations of Linear and Exponential FunctionsGraph the following functions of f(x) + k given the graphs of ƒ(x).

1. f(x) + 2

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2. f(x) – 3

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continued


NAME:


© Walch Education


1. f(x) + 2

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2. f(x) – 3

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continued

2.)


NAME:


© Walch Education


1. f(x) + 2

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2. f(x) – 3

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continued

3.)


NAME:


© Walch Education

5. Given the graphs of f(x) and g(x) below, write a function rule for g(x) in terms of f(x).

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f(x)

g(x)


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10

f(x)

g(x)

continued

4.)


NAME:



-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

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g(x)

f(x)


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f(x)

g(x)

continued

Independent Practice


NAME:


Problem-Based Task 3.7.2: Gym FeesPaulo and Justin belong to the same gym. The graph below shows how much each man pays per month in gym fees. Both pay the same per-hour use fee, but Paulo gets an employee discount, so his monthly membership fee is different from Justin’s membership fee. What is a function rule that represents Paulo’s total monthly gym fees? What is a function rule that represents Justin’s total monthly gym fees? What is the difference in their fees?

0 5 10 15 20 25 30 35 40 45 50

5

10

15

20

25

30

35

40

45

50

Paulo

Justin

Tota

l mon

thly

cos

t ($)

Monthly hours of gym use

Homework

1. )

2.)


NAME:


© Walch Education

9. f(x) = 2x + 1 and g(x) = 2x – 2. If g(x) can be written as f(x) + k, what is the value of k?

10. f(x) = 2x – 1 and g(x) = 2x + 3. If g(x) can be written as f(x) + k, what is the value of k?


NAME:


© Walch Education

9. f(x) = 2x + 1 and g(x) = 2x – 2. If g(x) can be written as f(x) + k, what is the value of k?

10. f(x) = 2x – 1 and g(x) = 2x + 3. If g(x) can be written as f(x) + k, what is the value of k?

name: 6/*5 t 3.7.2%transformations%of%linear...

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