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


Sketch . 

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

  1. 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.

  2. Shift to the left units and down units. Write the new equation, , as an absolute value function.

    This is .
    Change the domain for the horizontal shift only.

  3. 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?