Describe how the graph of y = x4 can be transformed to the graph of the given equation.
y = (x – 2)4 + 9 (5 points)
Shift the graph of y = x4 right 2 units and up 9 units.
Shift the graph of y = x4 left 2 units and down 9 units.
Shift the graph of y = x4 right 2 units and down 9 units.
Shift the graph of y = x4 left 2 units and up 9 units.
2.
Use your calculator and a table of values to find the exact value of . (The limit as x approaches zero) (5 points)
3.
Use the graph below to evaluate :
(5 points)
0
4
3
2
4.
Find the vertical asymptote(s) for the function . (5 points)
x = -5, 5
y = 0
x = -1
x = 5
5.
The end behavior of most closely matches which of the following? (5 points)
y = 0
y = 1
y = 2
y = -18
6.
Which of the following functions is continuous at x = 2? (5 points)
All are continuous at x = 2
7.
Evaluate . (5 points)
108
3
81
Does not exist
8.
Find f ‘(x) for f(x) = 8x3 + 2x2 – 8x + 10. (5 points)
None of these
f ‘(x) = 24x2 + 4x – 8
f ‘(x) = 24x2 + 4x – 8 + 10
f ‘(x) = 24x + 4x – 10
9.
Find g ‘(x) for g(x) = sec(2x). (5 points)
g ‘(x) = 2tan2(2x)
g ‘(x) = 2sec(2x)tan(2x)
g ‘(x) = 2sec(2x)
g ‘(x) = 2sec2(2x)
10.
Where is the second derivative of y = 2xe-x equal to 0? (5 points)
2
4
1
0
11.
If f(x) = arctan(2x), then f ‘(x) = ? (5 points)
12.
The graph of the derivative, f ‘(x) is shown below. On what interval is the graph of f (x) concave up?
(5 points)
Concave up on (-∞, -1)
Concave up on (-6, -2)
Concave up on (-∞, -∞)
Concave up on (-1, ∞)
13.
A particle moves along the x-axis with position function s(t) = ecos(x). How many times in the interval [0, 2π] is the velocity equal to 0? (5 points)
More than 3
2
3
1
14.
An ice block is melting so that the length of each side is changing at the rate of 1.5 inches per hour. How fast is the surface area of the ice cube changing at the instant the ice block has a side length of 2 inches? (5 points)
-18 in2/hour
-36 in2/hour
-12 in2/hour
-24 in2/hour
15.
If f(x) = |(x2 – 4)(x2 + 2)|, how many numbers in the interval [0, 1] satisfy the conclusion of the Mean Value Theorem? (5 points)
3
None
2
1
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