CPM Homework Help : PC3 Problem 7-36

Given the graph of the piecewise-defined function at right, complete the following limit statements or state that the limit does not exist. First & second quadrant piecewise graph, left piece, coming from lower left, opening up, ending at (negative 2, comma 2), center piece, downward parabola, vertex at (0, comma 5), starting at closed point (negative 2, comma 3), ending at closed point (2, comma 3), right piece, decreasing ray starting at closed point (2 comma 3), passing through (6, comma 1), continuing right & down.

$\lim\limits _ { x \rightarrow - \infty } f ( x ) =$
Hint (a):
What happens to the curve on the far left side?
$\lim\limits _ { x \rightarrow - 2 ^ { - } } f ( x ) =$
Hint (b):
What is the height of the function if you approach $x=-2$ from the left?
$\lim\limits _ { x \rightarrow - 2 ^ { + } } f ( x ) =$
Hint (c):
What is the height of the function if you approach $x=-2$ from the right?
$\lim\limits _ { x \rightarrow - 2 } f ( x ) =$
Hint (d):
Do your answers to parts (b) and (c) agree?
$\lim\limits_ { x \rightarrow 2 } f ( x ) =$
Hint (e):
Since the curve is continuous at $x=2$ , this is just $f(2)$ .
$\lim\limits _ { x \rightarrow \infty } f ( x ) =$
Hint (f):
What happens to the curve on the far right side?