A function is defined by f(x)= cases ax+b, & x 1

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

Problem

A function

f

is defined by

f(x)=\begin{cases} ax+b, & x\le1,\\ x^2+a, & 1<x<4,\\ 6x-b, & x\ge4. \end{cases}

Determine the ordered pair

(a,b)

that makes

f

continuous at both

x=1

and

x=4

. (a)

(8,0)

(b)

(9,1)

(c)

(7,1)

(d)

(2,6)