CPM Homework Help : PC3 Problem 7-87

3 piece, piecewise, y axis unscaled, left piece, linear from lower left to open point @ x = negative 2, center opening up curve, starting at same open point at x = negative 2, decreasing then turning on the y axis, ending @ open point @ x = 2, right piece, decreasing ray, starting at same open point at x = 2, continuing right & down. The graph of $y=g(x)$ is shown at right. Does $\lim\limits _ { x \rightarrow b } g ( x )$ exist for:

Hint:

Limits do not exist when there are vertical asymptotes or "jumps" in the curve.

$b=-3$ ?
$b=-2$ ?
$b=2$ ?
All values of $b$ in the interval $-3<b<5$ ?
Is the function continuous at $x=2$ ? Explain.
Hint (e):
For a function to be continuous at a given point, the limit must exist and the function must be defined at that point.