The function f(x)= cases kx^ 2 +1, & x 1, 3x+c, & 1< x <3, 10, & x 3 cases is…

MATHEMATICS · Single correct · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

The function

f(x)= \begin{cases} kx^{2}+1, & x\le 1,\\ 3x+c, & 1< x <3,\\ 10, & x\ge 3 \end{cases}

is required to be continuous at both

x=1

and

x=3

. Which of the following pairs

(k,c)

satisfies this requirement? (a)

(4,1)

(b)

(3,1)

(c)

(1,3)

(d)

(3,0)