Absolute Value Functions

An absolute value function is a function that returns the non-negative value of a number, represented as $$f(x) = |x|$$ .

The parent function of absolute value is $$f(x) = |x|$$ , which has a V-shaped graph opening upwards.

A vertical shift moves the graph up or down. For example, $$f(x) = |x| + 2$$ shifts the graph up by 2 units.

A horizontal shift moves the graph left or right. For example, $$f(x) = |x - 3|$$ shifts the graph right by 3 units.

A negative sign indicates a reflection over the x-axis. For example, $$f(x) = -|x|$$ reflects the graph of the parent function downwards.

The absolute value of a number x is represented as $$|x|$$ .

Multiplying by a positive constant stretches the graph vertically. For example, $$f(x) = 2|x|$$ stretches the graph by a factor of 2.

Subtracting a constant shifts the graph down. For example, $$f(x) = |x| - 3$$ shifts the graph down by 3 units.

This function represents a left shift by 4 units and a downward shift by 5 units.

The vertex of an absolute value function $$f(x) = a|x - h| + k$$ is the point (h, k).