Define the function by h(x)= cases x^2-4, & x 2

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

Problem

Define the function

h

h(x)=\begin{cases} x^2-4, & x\le 2,\\ k - x, & x>2, \end{cases}

where

k

is a constant. (a) Determine the value of

k

that makes

h

continuous at

x=2

. (b) Using your value of

k

, evaluate

h(-3)

and

h(6)

. Explain why the equation

h(x)=0

must have at least one real solution on

(-3,6)

. (c) Identify two consecutive integers between which a solution to

h(x)=0

is guaranteed to lie, and justify your choice.