Question

Sketch the graph of the function.
f(x) =

4 + x if x < -2
x2 if -2 = x < 2
6 - x if x = 2




Use the graph to determine the values of a for which
lim
x ? a
f(x)
does not exist. (Enter your answers as a comma-separated list.)
a =

Answer 1

I'm going to assume you meant x² if -2 < x < 2

In order for a limit to exist, f(a) must exist, limf(a) x-->a must exists, and limf(a) x-->a must equal f(a)

By looking at the graph, the limit of -2 does not exist because there's a jump discontinuity and the left and right limits are not equal

a = -2