The Algebra Teacher\'s Guide to Reteaching Essential Concepts and Skills

Name Date

WORKSHEET 8.6: DESCRIBING VERTICAL SHIFTS OF THE

GRAPH OF A FUNCTION

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Equations can be used to represent the vertical shifts of the graph of a function. Follow the

steps below:

1. Find the basic function the equation describes.


2. Compare the equation toy=f(x)+d.
   
   
   • Ifd>0, the graph is shifted up.
   
   
   • Ifd<0, the graph is shifted down.
   
   
   • Ifd= 0 ,thegraphisnotshiftedupordown.
   
   
   
   

EXAMPLE

Describe the graph off(x)=

√

x− 3.

The graph is the same as the graph of the square root function but it is shifted down 3 units

becaused=− 3.

DIRECTIONS: Describe the graph of each function.

1. f(x)=

1

x

+ 3 2. g(x)=x^3 − 2 3. h(x)=x^2 − 4

4. I(x)=|x| 5. j(x)=

√

x+ 2 6. F(x)=x− 1

CHALLENGE:Felipe said that when the graph of a function is moved vertically,

the domain and range also change. Do you agree? Explain your answer.

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Copyright

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2011 by Judith A. Muschla, Gary Robert Muschla, and Erin Muschla. All rights reserved.