CPM Homework Help : CALC Problem 4-152

Find the value for $a$ below so that $f(x)$ is continuous at $x = 3$ .

$f ( x ) = \left\{ \begin{array} { c c } { | 4 - 3 x | } & { \text { for } x < 3 } \\ { a x ^ { 2 } + 2 } & { \text { for } x \geq 3 } \end{array} \right.$

Hint:

We need to find a value of $a$ such that:

Step 1:

Substitute the left piece of $f(x)$ and the right piece of $f(x)$ .

Step 2:

Evaluate the limits: $5 = 9a + 2$

Answer:

Solve for $a$ :