Precalculus Fall Pre/Post Test
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Determine whether the graph is the graph of a function.
1)
x
-10
-5
5
10
y
10
5
-5
-10
A) Yes
B) No
1)
Match the function with the graph.
2)
x
-10
10
y
10
-10
A) y = ∣x - 1∣
B) y = ∣x - 1∣ + 1
C) y = ∣x∣ - 1
D) y = ∣x + 1∣
2)
3)
x
-5
-4
-3
-2
-1
1
2
3
4
5
y
10
5
-5
-10
A) y = x3 + 2
B) y = x3 - 2
C) y = (x - 2)3
D) y = x3
3)
1
Find the domain of the given function.
4) f(x) = 9 - x
A) All real numbers
B) (-∞, 9]
C) ( 9,∞)
D) (-∞,9) ∪ (9,∞)
4)
5) f(x) = (x + 3)(x - 3)
x2 + 9
A) (-∞,-9) ∪ (-9,9) ∪ (9,∞)
B) All real numbers
C) (-∞,3) ∪ (-3,3) ∪ (3,∞)
D) (9,∞)
5)
Describe how to transform the graph of f into the graph of g.
6) f(x) = x and g(x) = - x + 3
A) Shift the graph of f left 3 units and then reflect across the y-axis.
B) Shift the graph of f up 3 units and then reflect across the y-axis.
C) Shift the graph of f left 3 units and then reflect across the x-axis.
D) Shift the graph of f right 3 units and then reflect across the x-axis.
6)
Fill in the blanks to complete the statement.
7) The graph of y = - 5
6

3
x + 9 can be obtained from the graph of y =
3
x by shifting horizontally ?
units to the ? , vertically shrinking by a factor of ? , and then reflecting across the ? -axis.
A) 9; right; 5/6; x
B) 9; right; -5/6; y
C) 9; left; 5/6; x
D) 5/6; right; 9; y
7)
8) The graph of y = -9x3 + 2 can be obtained from the graph of y = x3 by vertically stretching by a
factor of ? ; reflecting across the ? -axis, and shifting vertically ? units in the ? direction.
A) 2; x; 9; upward
B) -9; x; 2; downward
C) 9; x; 2; upward
D) 9; y; 2; upward
8)
2
Match the equation to the correct graph.
9) y = 2(x + 3)2 - 3
A)
x
-10-9-8-7-6-5-4-3-2-1 1 2 3 4 5 6 7 8 910
y
10
9
8
7
6
5
4
3
2
1
-1
-2
-3
-4
-5
-6
-7
-8
-9
-10
B)
x
-10-9-8-7-6-5-4-3-2-1 1 2 3 4 5 6 7 8 910
y
10
9
8
7
6
5
4
3
2
1
-1
-2
-3
-4
-5
-6
-7
-8
-9
-10
C)
x
-10-9-8-7-6-5-4-3-2-1 1 2 3 4 5 6 7 8 910
y
10
9
8
7
6
5
4
3
2
1
-1
-2
-3
-4
-5
-6
-7
-8
-9
-10
D)
x
-10-9-8-7-6-5-4-3-2-1 1 2 3 4 5 6 7 8 910
y
10
9
8
7
6
5
4
3
2
1
-1
-2
-3
-4
-5
-6
-7
-8
-9
-10
9)
Write the quadratic function in vertex form.
10) y = x2 + 4x + 7
A) y = (x - 2)2 - 3
B) y = (x - 2)2 + 3
C) y = (x + 2)2 + 3
D) y = (x + 2)2 - 3
10)
Determine if the function is a power function. If it is, then state the power and constant of variation.
11) f(x) = 1
7
x5
A) Power is 1
7
; constant of variation is 5
B) Power is 5; constant of variation is 1
7
C) Power is 5; constant of variation is 1
D) Not a power function
11)
Write the statement as a power function equation. Use k as the constant of variation.
12) p varies directly as r.
A) p = r
B) p = r + k
C) p = kr
D) p = k/r
12)
Divide using synthetic division, and write a summary statement in fraction form.
13) 2x
4 - x3 - 15x2 + 3x
x + 3
A) 2x3 + 5x2 + 3 +
9
x + 3
B) 2x3 - 5x2 + 3 + -9
x + 3
C) 2x3 - 7x2 + 6x -15 + - 45
x + 3
D) 2x3 - 7x2 + 6x -15 + 45
x + 3
13)
3
Find the remainder when f(x) is divided by (x - k)
14) f(x) = 7x4 + 12x3 + 6x2 - 5x + 16; k = 3
A) 1704
B) 2512
C) 946
D) 188
14)
For the given function, find all asymptotes of the type indicated (if there are any)
15) f(x) = (x - 4)(x + 9)
x2 - 1
, vertical
A) x = 4, x = -9
B) x = -4, x = 9
C) None
D) x = 1, x = -1
15)
Compute the exact value of the function for the given x-value without using a calculator.
16) f(x) = 1
3
x
for x = -1
A) 3
B) - 1
3
C) -3
D) 1
3
16)
Solve the equation.
17) 2(5 - 3x) = 1
16
A) 1
8
B) 8
C) 3
D) -3
17)
Find the exponential function that satisfies the given conditions.
18) Initial mass = 15 g, decreasing at a rate of 3.9% per day
A) m(t) = 15 ∙ 1.39t
B) m(t) = 3.9 ∙ 0.85t
C) m(t) = 15 ∙ 1.039t
D) m(t) = 15 ∙ 0.961t
18)
Evaluate the logarithm.
19) log7(
1
49
)
A) 2
B) 7
C) -7
D) -2
19)
Simplify the expression.
20) eln(0.2)
A) 0.2
B) e0.2
C) -0.2
D) ln(0.2)
20)
Solve the equation by changing it to exponential form.
21) log 2 x = -4
A) x = 1
24
B) x = - (4)2
C) x = -
4
log24
D) x = -2∙4
21)
Assuming all variables are positive, use properties of logarithms to write the expression as a sum or difference of
logarithms or multiples of logarithms.
22) log4 (xy)
A) log2 x + log2 y
B) log4 x - log4 y
C) log4 x + log4 y
D) log2 x - log2 y
22)
4
Use the change of base rule to find the logarithm to four decimal places.
23) log6 2
A) 0.7737
B) 2.5850
C) 0.3869
D) -0.3869
23)
Find the exact solution to the equation.
24) 57x = 625
A) x = 625
B) x = 4
7
C) x = 1024
D) x = 7
4
24)
Convert the angle to decimal degrees and round to the nearest hundredth of a degree.
25) 43°38′
A) 43.38°
B) 43.76°
C) 43.63°
D) 44.63°
25)
Convert the angle to degrees, minutes, and seconds.
26) 61.37°
A) 61°22′12′′
B) 61°22′37′′
C) 61°22′0′′
D) 61°22′18′′
26)
Convert from degrees to radians. Use the value of π found on a calculator and round answers to four decimal places, as
needed.
27) 45°
A) π
4
B) π
3
C) π
6
D) π
5
27)
Convert the radian measure to degree measure. Use the value of π found on a calculator and round answers to two
decimal places.
28) π/5
A) 0.628°
B) 36π°
C) 36°
D) (π/5)°
28)
Use the arc length formula and the given information to find the indicated quantity.
29) r = 4 in., θ = 11 rad; find s
A) 4
11
in.
B) 11
4
in.
C) 88 in.
D) 44 in.
29)
Find the exact values of the indicated trigonometric functions. Write fractions in lowest terms.
30)
13
5
12
Find tan A and cot A.
A) tan A = 13
5
; cot A = 13
12
B) tan A = 12
5
; cot A = 5
12
C) tan A = 5
12
; cot A = 12
5
D) tan A = 5
13
; cot A = 12
13
30)
5