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

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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


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

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