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

Name Date

WORKSHEET 8.7: DESCRIBING HORIZONTAL AND VERTICAL

SHIFTS OF THE GRAPH OF A FUNCTION

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Equations can be used to represent the horizontal shifts and vertical shifts of a function.

Follow the steps below:

1. Find the basic function the equation describes.


2. Compare the equation toy=f(x−c)+d.cindicates a horizontal shift.dindicates a
   vertical shift.


3. Find the values ofcandd.
   
   
   • Ifc>0, the graph is shifted to the right.
   
   
   • Ifc<0, the graph is shifted to the left.
   
   
   • Ifc= 0 , the graph is not shifted right or left.
   
   
   • Ifd>0, the graph is shifted up.
   
   
   • Ifd<0, the graph is shifted down.
   
   
   • Ifd= 0 ,thegraphisnotshiftedupordown.
   
   
   
   

EXAMPLE

Describe the graph off(x)=|x+ 4 |− 2.

The graph is the same as the graph of the absolute value function but it is shifted 4 units to

the left (c=− 4 ) and 2 units down (d=− 2 ).

DIRECTIONS: Describe the graph of each function.

1. f(x)=(x−1)^2 + 2 2. g(x)=(x−2)^3 − 5 3. F(x)=

1

x+ 3

4. h(x)=

1

x

• 3 5. j(x)=|x+ 1 |− 4 6. I(x)=

√

x+ 2 − 6

CHALLENGE:Mikal said that the graph off(x)=x+2 is the graph of the

identity function shifted up 2 units. Annie said that the graph is the graph of

the identity function shifted 2 units to the right. Who is correct? Explain

your answer.

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Copyright

©

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