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| PAGE: 348 | SET: Exercises | PROBLEM: 1 |
First find the minimum point of the graph.
Since absolute value function can not be negative, the minimum
point of the graph is where 
.
The original function is 
.
Set original function
(Add 8 to each side)
(Apply additive inverse property: 
)
(Apply additive identity property: 
)
Next make at table, fill out the table with values for x > 8 and x < 8.
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f(x) = | x | – 8 |
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|
x |
f(x) |
|
– 2 |
– 6 |
|
–1 |
– 7 |
|
0 |
– 8 |
|
1 |
– 7 |
|
2 |
– 6 |
First, draw a co-ordinate plane.
Locate the points on co-ordinate plane and draw the graph through these points.
=abs(x)-8.gif)
Graph for the absolute value function 
=abs(x).gif)
Observe the graphs, both graphs have same shape and
points on are 8 units lower than the points on .
The graph of is the graph of 
and translated 8 units down.
The graph of is the graph of and translated 8 units down.
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