### Home > APCALC > Chapter 6 > Lesson 6.5.1 > Problem6-178

6-178.

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

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

The Three Conditions of Continuity

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

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

Solve for $a$.

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