CPM Homework Help : APCALC Problem 1-113

Write a piecewise-defined function that will generate the graph at right.

Step 1:

Notice that there are two pieces that meet at $x = 5$ . So the boundary will be $x = 5$ .

Step 2:

Examine the first piece. What parent graph does it resemble? What transformation has been made? Write its equation.

Step 3:

Examine the second piece. What parent graph does it resemble? What transformation has been made? Write its equation.

Step 4:

Since the $y$ -intercept and the point $(9,6)$ are given on the graph, you can check your work for steps 2 and 3. Here's how: Substitute $(0,6)$ to the first piece (does it work?) Substitute $(9,6)$ to the second piece (does it work?)

Step 5:

Assemble the piecewise function. Remember that the boundary is $x = 5$ .

Use the eTool below to view the graphs.
Click the link at right for the full version of the eTool: Calc 1-113 HW eTool

First quadrant continuous piecewise, starting at (0, comma 6), increasing curve opening down, turning at (2, comma 8), continuing to decrease & open down to (5, comma 3.5), turning, increasing, opening down passing through highlighted point (9, comma 6), continuing up & right.