The piecewise function h(x)= cases |x-3|, & x<3

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

Problem

The piecewise function

h(x)=\begin{cases} |x-3|, & x<3,\\ ax+b, & x\ge 3 \end{cases}

contains two unknown real parameters

a

and

b

. In addition to requiring continuity at

x=3

, suppose the function value is specified to be

h(5)=7

. (1) Part 1: (a) Write an equation in

a

and

b

that follows from the condition that

h

is continuous at

x=3

. Show how this equation is obtained using limits. (2) Part 2: (b) Write a second equation in

a

and

b

implied by the condition

h(5)=7

. (3) Part 3: (c) Solve the system of equations from parts (a) and (b) to find the unique ordered pair

(a,b)