Construct a function defined on the interval whose graph satisfies all the following…

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

Problem

Construct a function

k

defined on the interval

-3\le x\le 3

whose graph satisfies all the following conditions: (i) On graph paper, draw one possible graph of

k

that meets all the above conditions for

-3\le x\le 3

. Clearly indicate open and closed points. (ii) For each of the points

x=0

and

x=2

, state the left–hand limit, right–hand limit (if applicable), the value of the function (if it exists), and explain why

k

is or is not continuous there. (iii) Briefly describe how you ensured continuity of

k

at all other points.