Question

If the function \( f(x) \), defined below, is continuous on the interval \([0,8]\), then: \[ f(x) = \begin{cases} x^2 + ax + b, & 0 \leq x < 2 \\ 3x + 2, & 2 \leq x \leq 4 \\ 2ax + 5b, & 4 < x \leq 8 \end{cases} \]

• A. a = 3, b = −2
• B. a = −3, b = 2
• C. a = −3, b = −2
• D. a = 3, b = 2

Hint:

Continuity at a point requires matching left-hand and right-hand limits.