An absolute value function is a function that contains an absolute value expression.
An absolute value graph has a distinct V-shape. It is symmetric about the vertical line that passes through its vertex. The vertex of an absolute value function is the point where the graph changes direction.
Graph the absolute value function f(x)=∣x−2∣−3 using a table of values.
x=-3
Subtract term
∣-5∣=5
Subtract term
x | ∣x−2∣−3 | f(x) |
---|---|---|
-2 | ∣-2−2∣−3 | 1 |
-1 | ∣-1−2∣−3 | 0 |
0 | ∣0−2∣−3 | -1 |
1 | ∣1−2∣−3 | -2 |
2 | ∣2−2∣−3 | -3 |
3 | ∣3−2∣−3 | -2 |
4 | ∣4−2∣−3 | -1 |
5 | ∣5−2∣−3 | 0 |
6 | ∣6−2∣−3 | 1 |
7 | ∣7−2∣−3 | 2 |
To draw the graph, we can plot these points, then connect them with a V-shaped curve.
x=1
Multiply
Subtract term
∣-3∣=3