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:
- Find the basic function the equation describes.
- Compare the equation toy=f(x−c)+d.cindicates a horizontal shift.dindicates a
vertical shift. - 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.
- f(x)=(x−1)^2 + 2 2. g(x)=(x−2)^3 − 5 3. F(x)=
1
x+ 3
- 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.