Graph an absolute value function
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You can quickly graph an absolute value function using the vertex and a table of values.
Note that the vertex is the sharp corner of the graph!
Example #1
Graph f(x) = |2x + 6|
The general form of the function is f(x) = |mx + b| + c
Using f(x) = |2x + 6|, m = 2, b = 6, and c = 0
First, find the vertex.
As seen in the lesson about absolute value function, the vertex is located at (-b / m, c)
Therefore, the vertex is (-6 / 2, 0) or (-3, 0)
Now, evaluate the function for several selected values of x.
| x | -5 | -4 | -2 | -1 | 0 |
| f(x) | 4 | 2 | 2 | 4 | 6 |
The graph of the absolute value function is shown below
Example #2
Graph f(x) = |-3x + 15| + 1
The general form of the function is f(x) = |mx + b| + c
Using f(x) = |-3x + 15| + 1, m = -3, b = 15, and c = 1
First, find the vertex.
The vertex is located at (-b / m, c) or (-15 / -3, 1) or (5, 1)
The vertex is (-6 / 2, 0) or (-3, 0)
Now, evaluate the function for several selected values of x.
| x | 3 | 4 | 6 | 7 |
| f(x) | 7 | 4 | 4 | 7 |
The graph of the absolute value function is shown below
