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pages 455–456 for exercise sets.
y
x
f(x) |x|
f(x) |x 2|
f(x) |x 2|
y
x
f(x) |x|
f(x) |x| 3
f(x) |x| 3
1.Graph the absolute-value functions f(x) |x| 2 and f(x) |x| 2.
Explain how their graphs are related to the graph of f(x) |x|.
2.Graph the function f(x) |x|. Compare this graph to the graph of f(x) |x|.
3.Discuss and Write If c0, describe how the graphs of f(x) |xc| and
f(x) |x| ccompare to the graph of f(x) |x|.
- Compare the graphs of f(x) |x2| and f(x) |x2| with the graph
of f(x) |x|. Make a table of values for each and then plot the points
on the same axes as your graph of f(x) |x|. Connect the points for each
function to get the graphs shown below.
All three graphs have the same shape, but they have
different vertices.
The graph of f(x) |x2 | is the graph of f(x) |x|
translated left 2 units.
The graph of f(x) |x2| is the graph of f(x) |x|
translated right 2 units.
- Compare the graphs of f(x) |x| 3 and f(x) |x| 3 with the graph of f(x) |x|.
Make a table of values for each and then plot the points on the same axes as the
graph of f(x) |x|.
As before, the graphs have the same shape but
different vertices. The graph of f(x) |x| 3 is the
graph of f(x) |x| translated up 3 units. The graph
of f(x) |x| 3 is the graph of f(x) |x| translated
down 3 units.
f(x) |x| 3
Input
x
Output
f(x)
25
14
03
14
25
f(x) |x| 3
Input
x
Output
f(x)
63
30
0 3
30
f(x) |x 2|
Input
x
Output
f(x)
42
20
02
24
f(x) |x 2|
Input
x
Output
f(x)
46
24
02
20
42
