CPM Homework Help : APCALC Problem 6-178

Given the piecewise-defined function below, what value of $a$ will make this function continuous? .

$f ( x ) = \left\{ \begin{array} { l l } { \sqrt { 1 - x } + 7 } & { \text { for } x > - 3 } \\ { - a x ^ { 3 } } & { \text { for } x \leq - 3 } \end{array} \right.$

Hint:

The Three Conditions of Continuity

$1. \lim \limits_{x \rightarrow a} f(x) \text{ exists} \\ 2. f(a) \text{ exists}\\ 3. \lim \limits_{x \rightarrow a} f(x) =f(a)$

Step:

$\sqrt{1-(-3)}+7=-a(-3)^{3}$

Solve for $a$ .

Use the eTool below to visualize the problem.
Click the link at right for the full version of the eTool: Calc 6-178 HW eTool