Plot the function
f(x)= { x+5
|2x| - 2
-3
-5 ≤ x ≤ -1
-1 < x 1
1 ≤ x ≤ 5

Evaluate each x values for each function.

If the x value is from -5 to -1, f(x) = x + 5
Substituted function
f(-5) = -5 + 5 = 0
f(-4) = -4 + 5 = 1
f(-3) = -3 + 5 = 2
f(-2) = -2 + 5 = 3
f(-1) = -1 + 5 = 4
Point
(-5, -0)
(-4, 1)
(-3, 2)
(-2, 3)
(-1, 4)
If the x value is between -1 to 1, f(x) = |2x| - 2
f(-1) = |2(-1)| - 2 = 0
f(0) = |2(0)| - 2 = -2
f(1) = |2(1)| - 2 = 0
(-1, 0)
(0, -2)
(1, 0)
If the x value is from 1 to 5, f(x) = -3
f(1) = -3
f(2) = -3
f(3) = -3
f(4) = -3
f(5) = -3
(1, -3)
(2, -3)
(3, -3)
(4, -3)
(5, -3)
Here is the graph:
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Click to enlarge

Notice that points (-1,0) and (1,0) are hollow points. It means these points are not included in the range.


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