AFM
Polynomial & Power Function Exam
Study Guide
Name___________________________________
Date_________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Determine if the function is a power function. If it is, then state the power and constant of variation.
1
1) f x = x2
2
1)
1
; constant of variation is 2
2
A) Not a power function
B) Power is
C) Power is 2; constant of variation is 2
D) Power is 2; constant of variation is
1
2
2) f x = 3x-3/4
2)
3
A) Power is - ; constant of variation is 3
4
C) Power is
B) Not a power function
3
; constant of variation is 3
4
D) Power is 3; constant of variation is -
3) f x = -7
A) Power is -7; constant of variation is 0
C) Not a power function
3
4
3)
B) Power is 0; constant of variation is 7
D) Power is 0; constant of variation is -7
Determine if the function is a monomial function (given that c and k represent constants). If it is, state the degree and
leading coefficient.
4) f x = 4 · x-6
4)
A) Degree is 6; leading coefficient is 4
C) Not a monomial function
5) I(d) =
B) Degree is -6; leading coefficient is 4
D) Degree is 4; leading coefficient is -6
k
5)
d2
A) Degree is -2; leading coefficient is k
C) Not a monomial function
B) Degree is 2; leading coefficient is k
D) Degree is 2; leading coefficient is I
6) f x = -9
A) Not a monomial function
C) Degree is -9; leading coefficient is 0
6)
B) Degree is 0; leading coefficient is -9
D) Degree is 1; leading coefficient is -9
Write the statement as a power function equation. Use k as the constant of variation.
7) p varies directly as r.
A) p = k/r
B) p = r + k
C) p = r
8) The area of an equilateral triangle varies directly as the square of the side s.
s2
k
A) A =
B) A = ks2
C) A =
k
s2
1
7)
D) p = kr
8)
D) A = k2 s
Match the equation to one of the curves (for x ≥ 0).
3
9) f x = x-5
4
9)
y
x
A)
B)
y
y
x
x
C)
D)
y
y
x
x
Solve the problem.
10) The table shows the population of a certain city in various years. The population of the city f(x), in
hundreds of thousands, can be modeled by f(x) = axb, where x represents the number of years since
1980. Estimate the population of the city in the year 1998. (You will first need to use regression to
estimate the values of a and b).
Year
1981 1985
Population (hundreds of thousands) 3.2
4.1
A) 1,106,995
B) 1,146,530
1989 1993 1997
5.7 9.6 14.1
C) 1,041,856
2
D) 988,388
10)
Solve the problem. Round as appropriate.
11) The gravitational attraction A between two masses varies inversely as the square of the distance
between them. The force of attraction is 4 lb when the masses are 3 ft apart, what is the attraction
when the masses are 6 ft apart?
A) 2 lb
B) 4 lb
C) 3 lb
D) 1 lb
11)
Data are given for y as a power function of x. Write an equation for the power function, and state its power and constant
of variation.
2 4
6
8
10
12) x 1
12)
y -16 -4 -1 -0.444... -0.25 -0.16
16
A) y =
; Power = -4; constant of variation = 16
x2
B) y = -
16
; Power = -1; constant of variation = -16
x
C) y = - 16x ; Power = 1; constant of variation = -16
16
D) y = ; Power = -2; constant of variation = -16
x-2
13) x 1
y 2
8
4
A) y =
B) y = 2
C) y = 2
27
6
125 216
10
12
1
x ; Power = ; constant of variation = 1
2
3
3
64
8
13)
x ; Power = -3; constant of variation = 2
x ; Power =
1
; constant of variation = 2
3
D) y = 0.5x ; Power = 1; constant of variation = 0.5
Write the statement as a power function equation. Use k as the constant of variation.
14) The cost c of a turkey varies directly as its weight w.
w
A) c =
B) c = kw2
C) c = kw
k
Match the given graph with its polynomial function.
15)
14)
k
D) c =
w
15)
A) f(x) = x5 + 4x3 - x2 + 3x - 5
C) f(x) = -x3 + 4x2 + x - 5
B) f(x) = x3 + 4x2 - x - 5
D) f(x) = x3 + x2 + x + 5
3
16)
16)
A) f(x) = 2x3 - 12x2 - 5x - 12
C) f(x) = -3x5 + 2x4 - x2 + 2x - 12
B) f(x) = -3x3 - 10x2 + 5x + 12
D) f(x) = x4 - 2x2 - 3x + 12
17)
17)
A) f(x) = 2x5 + x3 + 8x2 - 4x + 3
C) f(x) = -3x5 + x4 + 2x
B) f(x) = -x4 + x3 - x
D) f(x) = 2x4 + x3 - 3x2 - 6x
18)
18)
A) f(x) = x5 - 4x3 + 12x2 + 10
C) f(x) = x4 + x3 - 10x2 + 10
B) f(x) = -x4 + x3 - 12x2 + 10
D) f(x) = -x5 - 10x2 - 10
19)
19)
A) f(x) = x4 - 5x3 + 6x2 + x + 10
C) f(x) = -x3 + 15x2 + x - 10
B) f(x) = -x5 - 5x3 - 6x2 + 10x
D) f(x) = x5 + 3x4 - 5x3 - 15x2 + x + 10
4
20)
20)
A) f(x) = -x6 + 7x5 - x2 - 2x + 16
C) f(x) = x5 + 7x4 - x3 - 40x2 + 2x + 16
B) f(x) = -2x5 + 7x4 + 9x3 - 40x2 + 4x + 16
D) f(x) = 2x6 + 9x3 - 7x2 + 4x - 16
21)
21)
A) f(x) = -x5 - 20x4 - 100x 2 + 100x
C) f(x) = x5 - 10x4 - 100x 2 + 100
B) f(x) = -x6 + 10x4 - 100x 2 - 100
D) f(x) = -x6 + 20x4 - 100x 2 + 100
22)
22)
A) f(x) = -x3 + 20x
C) f(x) = x3 + 9x
B) f(x) = -x3 + 4x2 - 9
D) f(x) = x3 - 4x2 + 20x
Graph the function in a viewing window that shows all of its extrema and x-intercepts.
5
23) f(x) = -3x(x + 2)(x - 1)
23)
y
x
A)
B)
y
y
10
10
-10
10
x
-10
-10
10
x
10
x
-10
C)
D)
y
y
10
-10
10
10
x
-10
-10
-10
6
24) f x = x + 1 x + 3 x - 2
24)
y
x
A)
B)
y
y
10
10
-10
10
x
-10
-10
10
x
10
x
-10
C)
D)
y
y
10
-10
10
10
x
-10
-10
-10
7
25) f x = x + 2 2 x - 1 x - 2
25)
y
x
A)
B)
y
y
10
10
-10
10
x
-10
-10
10
x
10
x
-10
C)
D)
y
y
10
-10
10
10
x
-10
-10
-10
Describe the end behavior of the polynomial function by finding lim f x and lim f x .
x→∞
x→-∞
26) f x = 6x4 - 2x2 + 10
A) -∞, ∞
B) -∞, -∞
C) ∞, ∞
D) ∞, -∞
27) f x = x3 - 3x2 + 7x + 3
A) ∞, -∞
B) -∞, ∞
C) ∞, ∞
D) -∞, -∞
28) f x = -x3 - 5x2 - 7x + 3
A) ∞, ∞
B) ∞, -∞
C) -∞, -∞
D) -∞, ∞
26)
27)
28)
8
29) f x = -4x2 + 3x3 + 2x + 2
A) -∞, -∞
B) -∞, ∞
C) ∞, -∞
D) ∞, ∞
30) f x = 4x2 - 4x3 + 2x - 9
A) -∞, -∞
B) ∞, ∞
C) ∞, -∞
D) -∞, ∞
29)
30)
Use a cubic or quartic regression (as specified) to fit a curve through the points given in the table. Round to the nearest
hundredth.
31) x -3 1 3 4 (Cubic)
31)
y 50 -3 -45 -102
A) y ≈ -1.53x3 + 0.24x2 - 2.07x + 0.36
B) y ≈ -1.53x3 + 0.24x2 - 2.57x + 0.36
C) y ≈ -1.53x3 + 0.54x2 - 2.07x + 0.36
D) y ≈ -1.83x3 + 0.24x2 - 2.07x + 0.36
32) x -2 0 1 3 (Cubic)
y 10 15 21 33
A) y ≈ 0.23x3 + 0.93x2 + 5.10x + 15.00
32)
B) y ≈ 0.23x3 + 0.73x2 + 5.30x + 15.00
D) y ≈ -0.23x3 + 0.73x2 + 5.10x + 15.00
C) y ≈ -0.23x3 + 0.93x2 + 5.30x + 15.00
33) x 2 3 5 6 7 (Quartic)
y 3 5 9 15 19
A) y ≈ -0.18x4 + 3.77x3 - 20.02x2 + 41.93x - 44.00
33)
B) y ≈ 0.16x4 + 3.77x3 + 20.02x2 + 51.93x - 44.00
C) y ≈ -0.18x4 + 3.27x3 - 20.02x2 + 51.93x - 44.00
D) y ≈ -0.18x4 + 3.27x3 + 20.02x2 + 55.93x - 46.00
Solve the problem.
34) A(x) = -.015x 3 + 1.05x gives the alcohol level in an average person's blood x hrs after drinking 8 oz
of 100-proof whiskey. If the level exceeds 1.5 units, a person is legally drunk. Would a person be
drunk after 4 hours?
A) Yes
B) No
34)
35) The polynomial function L(p) = p3 - 5p 2 + 20 gives the rate of gas leakage from a tank as pressure
increases in p units from its initial setting. Will an increase of 4 units result in a lower rate of
leakage compared to the initial setting?
A) Yes
B) No
35)
36) The polynomial function I(t) = -.1t2 + 1.8t represents the yearly income (or loss) from a real estate
investment, where t is time in years. After how many years does income begin to decline? Round to
the nearest tenth of a year, if necessary.
A) 12 years
B) 18 years
C) 9 years
D) 8 years
36)
37) The polynomial G(x) = -.006x 4 + .140x3 - 0.53x 2 + 1.79x measures the concentration of a dye in the
bloodstream x seconds after it is injected. Does the concentration increase between 11 and 12
seconds?
A) No
B) Yes
37)
9
Answer Key
Testname: POLYNOMIAL & POWER FUNCTION EXAM
1) D
2) A
3) C
4) C
5) C
6) B
7) D
8) B
9) B
10) C
11) D
12) D
13) C
14) C
15) B
16) B
17) D
18) C
19) D
20) B
21) D
22) A
23) D
24) B
25) B
26) C
27) A
28) D
29) C
30) D
31) A
32) C
33) C
34) A
35) A
36) C
37) B
10