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- Given the functions
f x
x
2
4 and g x
3 x 1 , find
f
g
A.
B.
C.
D.
E. None of the above
Use the graph of the function
y f x
, shown below, to answer questions #2 and #3:
- Find the intervals for which
f is increasing.
A. 3,
B. 1,
C. 4, 2
D. 3,
E. None of the above
- Find all values of
x such that
f x
A. 2,
B. 4, 2
C. 3,
D. 0,
E. None of the above
- Find the domain of the function
h x
2 x 8
x
2
4 x 5
. Express your answer in interval notation.
A. , 1
B. 4,
C. , 1
D. 4,
E. None of the above
- If the point
P 1,
is on the graph of the function
y f x
, find the corresponding point on the
graph of
y 3 f 2 x
A. 3,
B.
C.
D. 2,
E. None of the above
- Given that
f is a function such that
f 2
5 and f 1
3 , and
g is a function such that
g 3
8 and g 1
2 , find and simplify
g f
A. 5
B. 6
C. 8
D. 2
E. Cannot be determined
- Express the parabola
f x
2 x
2
4 x 5 in standard form.
2
2
2
2
2
A f x x
B f x x
C f x x
D f x x
E f x x
- Given
f x
x
2
3 , find and simplify
f a h
f a
h
, if
h 0.
A. 2 a h 6
B. h 6
C. 2 a h
D. h
E. None of the above
- Given below, on the left, is the graph of a basic function,
y f x
. The graph on the right was
obtained by shifting, reflecting, stretching, and/or compressing the basic graph. Which of the
following best describes the graph on the right?
A. y f x 2
B. y f x 3
C. y f x 2
D. y f x 3
E. y f x 3
- Solve the following inequality. Express your answer in interval notation.
x x
x
. None of the above
A
B
C
D
E
- Suppose
w is directly proportional to the product of
x and the square root of
y , and inversely
proportional to the sum of
v and z. If
x 2, y 9, v 4, and z 5, then w 5. Find the value
of the constant of proportionality,
k.
. is less than 5 . is between 5 and 6 . is between 6 and 7 . is between 7 and 8 . is greater than 8
A k
B k
C k
D k
E k
- A doorway has the shape of a parabolic arch and is 9 feet high at the center and 6 feet wide at the
base. If a rectangular box 7 feet high must fit through the doorway, what is the maximum width
the box can have? Choose the answer that best describes the solution(s).
- An open box is to be made from a rectangular piece of cardboard having dimensions 40 inches by
60 inches by cutting identical squares of area
x
2
from each corner and turning up the sides (see
the figure). Express the volume,
V , of the resulting box as a function of
x. Simplify your
function.
A. The maximum width of the
box is less than 3 feet.
B. The maximum width of the
box is between 3 feet and 4
feet.
C. The maximum width of the
box is between 4 feet and 5
feet.
D. The maximum width of the
box is more than 5 feet.
E. None of the above
A. 𝑉(𝑥) = 2400 𝑥
B. 𝑉(𝑥) = 𝑥( 40 − 𝑥)( 60 − 𝑥)
C. 𝑉(𝑥) = 4 𝑥( 20 + 𝑥)( 30 + 𝑥)
D. 𝑉
E. 𝑉
