### Home > PC3 > Chapter 11 > Lesson 11.1.2 > Problem 11-25

11-25.

Sketch

Graph two lines. Sketch the first one to the right of , the second one to the left of

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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. Shift

to the leftunits and down units. Write the new equation, , as an absolute value function.This is

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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?