CPM Homework Help : PC3 Problem 8-154

Write the equation of the line $y = ax + b$ so that $f$ is continuous.

$f ( x ) = \left\{ \begin{array} { l l } { x ^ { 3 } - 4 } & { \text { for } \quad x < - 1 } \\ { a x + b } & { \text { for } - 1 \leq x < 1 } \\ { x ^ { 2 } - 8 } & { \text { for } \quad x \geq 1 } \end{array} \right.$

Hint:

When $x = − 1$ , $x^{3} − 4 = ax + b$ .

When $x = 1$ , $ax + b = x^{2} − 8$ .

Step:

$\left(-1\right)^3-4=a\left(-1\right)+b$

$a\left(1\right)+b=\left(1\right)^2-8$