Welcome! Today we'll learn how to graph absolute value functions. The absolute value function creates a distinctive V-shaped graph. The most basic form is y equals the absolute value of x, which has its vertex at the origin and opens upward.
The first step in graphing an absolute value function is to identify the vertex. For the general form y equals a times the absolute value of x minus h plus k, the vertex is located at the point h comma k. Let's see how changing h and k moves the vertex and transforms our graph.
The second step is to find the axis of symmetry. This is a vertical line that passes through the vertex. For our function y equals the absolute value of x minus h plus k, the axis of symmetry has the equation x equals h. The graph is perfectly symmetric about this line, creating mirror images on both sides.
Now we choose points on both sides of the vertex and calculate their y-values. Let's work with the function y equals the absolute value of x minus 2 plus 1. We'll select x-values like 0, 1, 3, and 4, then substitute them into our function to find the corresponding y-coordinates. This gives us the points we need to plot our V-shaped graph.