What is an absolute value function? 

• An absolute value function is a piecewise function whose graph has a “V” shape.
• The vertex form of an absolute value graph function is y = a | x – h | + k
• x and y represent the x-and y-coordinates of any point that lies on the graph
• The constants a, h, and k are called the parameters of the absolute value equation. These constants reveal the shape and location of the graph.
• The most basic absolute value function is y = | x | and is called the parent function.

You may also see it written in function notation as f(x) = | x |

• You can graph it by taking a ray and reflecting it across the vertical line (axis of symmetry) that passes through the ray’s endpoint.

• It is called the absolute value parent function because other absolute value functions can be found by transforming y = | x |.

The affects of “a” on the graph of the absolute value parent graph includes the following:

• whether the graph opens up or down,



• whether the graph is wider (compressed), narrower (stretched), or congruent to the parent function.

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