CPM Homework Help : INT3 Problem 3-114

Write a set of equations for the piecewise-defined function shown on the graph at right. Be sure to include the domain for each part of the function.

Hint:

Look at the two pieces of the function. One is a downward-facing parabola moved $2$ to the right, and the other is a line.

Answer:

$f(x)=\begin{cases}-(x-2)^2,x<2\\x+2,x\geq 2 \end{cases}$

Piecewise graph, 2 pieces: left, open circle at (2, comma 0), curve opens down, extends down and to the left, passing through (0, comma negative 4), with arrow on end. Right: Ray starts at closed point (2, comma 4), passing through (3 comma 5).