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AP® Calculus AB-BC

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Moderate

Piecewise Quadratic Function

APCALC-SS6KEU

Given the piecewise function:

$$f(x) = \left\{ {\begin{array}{*{20}{c}} {2{x^2} - 3x + 7}&{x \le 3}\\\ {{x^2} - 9}&{x > 3} \end{array}} \right.$$

Find any value(s) of $x$ where $f(x)$ is discontinuous and describe what kind of discontinuity it is.

A

Discontinuous at $x=3$; removable point discontinuity

B

Discontinuous at $x=3$; non-removable jump discontinuity

C

Discontinuous at $x=3$; non-removable infinite discontinuity

D

The function is continuous everywhere