Consider the function F(x)= cases |x|, & x 0

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

Problem

Consider the function

F(x)=\begin{cases} |x|, & x\le 0, \\ cx+d, & 0<x<2, \\ (x-2)^2+e, & x\ge 2, \end{cases}

where

c,d,e\in\mathbb{R}

. (a) Write the conditions that

c,d,e

must satisfy for

F

to be continuous at

x=0

. (b) Write the conditions that

c,d,e

must satisfy for

F

to be continuous at

x=2

. (c) Solve the system obtained in parts (a) and (b) to find all triples

(c,d,e)

for which

F

is continuous on the entire real line.