Graph, Domain and Range of Absolute Value Functions

This is a step by step tutorial on how to graph functions with absolute value. Properties of the graph of these functions such as domain, range, x and y intercepts are also discussed. Free graph paper is available.

Graph, Domain and Range of Absolute Value Functions; Examples with Detailed Solutions

Example 1:

f is a function given by
\[ f (x) = |x - 2| \]
  1. Find the x- and y-intercepts of the graph of \( f \).
  2. Find the domain and range of \( f \).
  3. Sketch the graph of \( f \).

Solution to Example 1

Example 2:

f is a function given by \[ f (x) = |(x - 2)^2 - 4| \]
  1. Find the x- and y-intercepts of the graph of \( f \).
  2. Find the domain and range of \( f \).
  3. Sketch the graph of \( f \).

Solution to Example 2

More References and Links to Graphing, Graphs and Absolute Value Functions