

x < −1
4 − x,
1. For what values of a is g(x) = 2,
x = −1 continuous?


1 − x2 + a, x > −1
2. Sketch the graph of a function that has the following properties:
• lim f (x) = 2
• lim− f (x) = −∞
x→−∞
•
•
x→0
lim f (x) = −1
• lim+ f (x) = 0
x→−3−
x→0
lim + f (x) = 2
• f (5) = 3
x→−3
• lim f (x) = ∞
• f (−3) = −1
x→∞
Based on the graph you just drew, what are the horizontal and vertical asymptotes if any?
3. lim+
t→2
|2 − t|
2−t
sin( 3r )
4. lim
r→π tan( r )
4
√
x+1−2
5. lim
x→3
3−x
√
4q 2 − q
6. lim √
q→∞ 3 q + 5q 2
7. What is the average rate of change of the function p(z) = −z 2 + 12z + 2 between the z values of -1 and
2.
8. The equation for how productivity of an employee is (R(t)) related to how much break time they have
(t), by R(t) = −x2 + 2020. If the perfect amount of break time is 30 minutes, what amount of
productivity is produced? If the productivity can vary by ±12 (tolerance), what is the largest amount
the break time can very from this perfect amount (error)?
9. True/False: If true explain why it is true, if false give a counterexample and explain why it is a
counterexample
(a) If f (4) = 1 and lim− f (x) = 1, then lim f (x) = 1.
x→4
x→4
(b) If lim Q(k) = 0, then lim Q(k) = 0.
k→∞
k→−∞
(c) The graph of a function with a vertical asymptote can never touch that asymptote.
(d) If f (w) is continuous on (−∞, ∞) and f (2) = −3, then lim+ f (w) = −3.
w→2