Lesson 7: Graphing Absolute Value Functions

Property

The absolute value function $f(x) = |x|$ creates a V-shaped graph with vertex at $(0, 0)$, opening upward with two linear pieces: $y = -x$ for $x < 0$ and $y = x$ for $x \geq 0$.

Examples

Property

The vertex of an absolute value function in the form $f(x) = a|x - h| + k$ is located at the point $(h, k)$. For functions not in vertex form, the vertex occurs where the expression inside the absolute value equals zero.

Examples

Property

To graph an absolute value function, create a table of values by selecting x-values around the vertex, then plot the ordered pairs $(x, y)$ and connect them to form the characteristic V-shape.

Examples

Property

The absolute value function $f(x) = |x|$ is symmetric about the y-axis, meaning $f(-x) = f(x)$ for all values of $x$. For transformed functions $g(x) = a|x - h| + k$, the axis of symmetry is the vertical line $x = h$ passing through the vertex.

Examples