Absolute value function

An absolute value function is a function of the form f(x) = |mx + b| + c, where m ≠ 0

For example, f(x) = |2x - 3| + 1 is an absolute value function with m = 2, b = -3 and c  = 1.

The graph of f(x) = |2x - 3| + 1 is shown below.

Graph of an absolute value function

Just like the graph above, graphs of absolute value functions look like angles.

The vertex of a function is a point where the function reaches a minimum or a maximum.

The vertex of f(x) = |mx + b| + c is located at (-b / m, c).

For example, using the function f(x) = |2x - 3| + 1, the vertex is located at (--3 / 2, 1) or (3 / 2, 1).

(3 / 2, 1) is the same as (1.5, 1). Looking at the graph above, we can clearly see that the vertex is located at (1.5,1) and it is a minimum.

Other examples of absolute value functions

1. y = |x| 

m = 1, b = 0, and c = 0

2. y = |x + 1|

m = 1, b = 1, and c = 0

3. y = |4x - 8| - 3

m = 4, b = -8, and c = -3

4. y = |-x|

m = -1, b = 0, and c = 0

5. y = |-x| - 8

m = -1, b = 0, and c = -8

6. y = |-3x + 5| - 4

m = -3, b = 5, and c = -4

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