Graph two lines. Sketch the first one to the right of
This graph should look like a function you have seen before, that is, the absolute value function. Write an equation for
using the absolute value function with the necessary transformations.
The general absolute value function is
, where is the vertex and a is the steepness of the two lines.
to the left units and down units. Write the new equation, , as an absolute value function.
Change the domain for the horizontal shift only.
Now write an equation for
using a piecewise-defined function. (Verify your solution by using a graphing calculator.) Compare this equation to the original equation for . What do you notice?