Apentix/AP Calculus AB/Unit 1: Limits and Continuity/Question

AP Calculus ABhardmcq1 pt

Let $f(x)=\begin{cases} x^2+ax, & x<1 \\ bx+3, & x>1 \end{cases}$ . If $f(1)=2$ and $f$ is continuous at $x=1$ , what is $a+b$ ?

A.

0

B.

1

C.

-1

D.

2

Explanation

Core Concept

Continuity requires the one-sided limits to equal $f(1)=2$ . From the left, $1+a=2$ , so $a=1$ . From the right, $b+3=2$ , so $b=-1$ . Thus $a+b=0$ .

Correct Answer

A $0$

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