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:
- Find the basic function the equation describes.
- 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.
- f(x)=
1
x
+ 3 2. g(x)=x^3 − 2 3. h(x)=x^2 − 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
©
2011 by Judith A. Muschla, Gary Robert Muschla, and Erin Muschla. All rights reserved.