A function is defined by g(x)= cases kx^2-5k, & x<3, [4pt] 2x+1, & x 3

MATHEMATICS · Multi-part · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

A function

g

is defined by

g(x)=\begin{cases} kx^2-5k, & x<3,\\[4pt] 2x+1, & x\ge 3, \end{cases}

where

k

is a real constant. (a) Determine the value of

k

that makes

g

continuous at

x=3

. (b) Using your value of

k

, verify algebraically that

g

is continuous at

x=3