7. Graphing Absolute Value Functions
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Graph a few absolute value functions with different values of a, h, and k to see how the vertex changes.
(ah,k)
As shown above, when a=2 the vertex becomes (21,1).
When a=41, the vertex becomes (4,1). Let's compare these functions and vertices.
a | f(x)=∣ax−1∣+1 | Vertex |
---|---|---|
1 | f(x)=∣x−1∣+1 | (1,1) |
2 | f(x)=∣2x−1∣+1 | (21,1) |
41 | f(x)=∣∣∣∣∣41x−1∣∣∣∣∣+1 | (4,1) |
We can see that we can create the x-coordinate of the vertex by dividing h or k by a. We can graph one more function with different values for h and k to confirm this. Let's graph the function f(x)=∣2x−4∣+3.