CPM Homework Help : APCALC Problem 2-130

A function, $f$ , is continuous for all real numbers. If $f(x) = \large\frac { x ^ { 2 } - 9 } { x + 3 }$ when $x\ne-3$ , then what must $f(-3)$ equal? Write a piecewise-defined function that represents this situation.

Hint:

After factoring, you will see that there is a hole (not a vertical asymptote) at $x=−3$ .

While $f(−3)$ does not exist, the

$\lim\limits _{x\rightarrow -3}f(x)$

exist, and gives us the $y$ -value of the hole.