### Home > PC3 > Chapter 6 > Lesson 6.2.3 > Problem6-116

6-116.

Determine the values of $a$ and $b$ such that $y = f \left(x\right)$ will be continuous for all values of $x$.

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

At $x = 2, 2x + a = x^{2} − 2$.

At $x = 3, x^{2} − 2 = −x + b$.