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

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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


  1. 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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2011 by Judith A. Muschla, Gary Robert Muschla, and Erin Muschla. All rights reserved.

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