CPM Homework Help : PC3 Problem 10-88

Use the graph of $y = f(x)$ at right to evaluate each of the following expressions.

$\lim\limits_ { x \rightarrow 2 ^ { - } } f ( x )$
Hint (a):
This is the limit as x approaches $2$ from the left. Start on the curve at $x = 0$ and move towards $x = 2$ . What height is the function approaching?

$\lim\limits_ { x \rightarrow 2 ^ { + } } f ( x )$
Hint (b):
This is the limit as $x$ approaches $2$ from the right.

$\lim\limits_ { x \rightarrow 2 } f ( x )$
Hint (c):
This limit exists if your answers to parts (a) and (b) are the same.

$f(2)$
Hint (d):
This is the value of the function at $x = 2$ . A function is not defined when there is an open dot.

Is the function continuous at $x = 2$ ? Use your answers to parts (a) through (d) to justify your conclusion.
Hint (e):
A function is continuous at a point if the limit exists and is equal to the function value at that point.

Curve, starting in lower left, opening down, passing through the point (negative 3, comma 0), turning at the open point (2, comma 3), passing through the point (5, comma 0), continuing down & right, & closed point at (2, comma 1).