Math 110 Test 3
Start Date: May 30
Late Fee: June 1
End Date: June 1
All Sections
No calculators, notes, or books.
DO NOT WRITE ON THIS EXAM
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Find the domain of the composite function f g.
-1
- 49
; g(x) =
1) f(x) =
x - 7
x
A) {x x 0, x
D) {x x 0, x
2) f(x) =
- 7}
7, x - 7}
x - 2; g(x) =
1)
B) {x x 0, x 7}
E) {x 0 < x < 7}
C) {x x > 0}
F) All real numbers
2
x - 10
A) {x - 2 x 2}
D) {x x 2, x 10}
2)
B) {x x > 10}
E) {x 10 < x 11}
C) {x x 10, x 2}
F) All real numbers
The function f is one- to- one. Find its inverse.
7
3) f(x) =
x + 5
A) f- 1 (x) =
5 + 7x
x
5 + 7x2
D) f- 1 (x) =
x
3)
B) f- 1 (x) =
7
x- 5
C) f- 1 (x) =
x
5 + 7x
E) f- 1 (x) =
- 5x + 7
x
F) f- 1 (x) =
7- x
5x
Find the domain of the function.
x + 9
4) f(x) = log10
x - 9
A) (- 9, 9)
D) (- , - 9)
4)
B) (- , - 9) (9, )
E) (9, )
C) {x x 9, x - 9}
F) All real numbers
Suppose than ln 2 = a and ln 5 = b. Use properties of logarithms to write ln 20 in terms of a and b.
5) ln 20
A) a + b
B) 2a + 2b
C) 5a
D) a- b
E) 4b
F) 2a + b
Express the following logarithm as a single logarithm.
1
6) (log3 (x - 5) - log3 x)
2
A) log3
x- 5
2x
B) log3
D) log3
x(x- 5)
E) log3
5)
6)
x- 5
x
x2
(x- 5)2
1
C) log3
F) log3
x- 5
x
x- 5
x
The graph of a logarithmic function is shown.
Select the function which matches the graph. Remember log x means log10 x.
7)
A) y = log(- x)
D) y = log x
8) 2
(5 - 3x)
=
8)
x- 5=
B) x=3
C) x=
1
8
D) x=8
E) x=-
1
3
1
3
F) x=
1
3
9)
A) x=- 1
B) x=262,149
D) x=9
E) x=
10) log3 x = 4- log3(x - 24)
A) x=27
D) x=12
11)
C) y = - log x
F) y = log 2x
1
16
A) x=- 3
9) log8
B) y = - log (x+1)
E) y = - log(- x)
7)
C) x=
16
3
109
9
F) x=14
10)
B) x=53
E) x=- 3 or x=27
C) x=6 or x=3
F) no solution
1
log (x + 6) = log (3x)
2
8
3
11)
3
4
A) x=3
B) x=9
C) x=
D) x=0 or x=- 3
E) x=5
F) no solution
2
Solve each exponential equation. Where applicable, express the solution in terms of natural logarithms.
x + 4
2x + 5
=5
12) 4
A) x=4 ln 4 - 5 ln 5
ln 4 - 2 ln 5
B) x=
5 ln 5 - 4 ln 4
D) x=ln 5 - ln 4
E) x=ln
55
4
4
4
52
C) x=7 ln 5 - 5 ln 4
F) x=
5 ln 5 - 4 ln 4
ln 4 - 2 ln 5
-x
13) e x = 3e +2
A) x=ln 3 or x=1
D) x=0
- 2- 5x
= 2x
2
A) x=5
14) ( 2)
13)
B) x=3 or x=- 1
E) x=ln 2
C) x=ln 3
F) x=2+ln 3
2
1
D) x= or x=0
2
14)
1
B) x=- or x=- 2
2
C) x=2
E) x=- 2 or x=- 5
F) no solution
Solve the problem.
15) How long will it take a sample of radioactive substance to decay to half of its original amount, if it
decays according to the function A(t) = 450e- 0.157t, where t is the time in years?
A)
.175
years
2
B)
D)
ln 2
years
.157
E) .175(ln 2) years
2
years
.157
F) 2 years
E) 5000(1.056)3
E) 12,000(1.0125)3
Find the equation of the parabola described.
18) Focus at (3, 0); directrix the line y = - 2
A) (x + 3)2 = 4(y + 1)
B) (y - 1)2 = 4(x - 3)
D) (x + 3)2 = 4(y - 1)
E) (x - 3)2 = 4(y - 1)
3
16)
F) 5000 e3(.056)
Find the amount that results from the investment.
17) $12,000 invested at 5% compounded quarterly a!er a period of 3 years
A) 12,000(1.05)12
B) 12,000 e12
C) 12,000(1.05)3
D) 12,000(1.0125)3/4
15)
C) (ln 2) years
16) Suppose that $5000 is invested at an interest rate of 5.6% per year, compounded continuously. What
is the balance a!er 3 years?
A) 5000e .056
B) 5000(1.56)3(.56)
C) e 5000(.056)
D) 5000 e3(5.6)
12)
17)
F) 12,000(1.0125)12
18)
C) (y + 1)2 = 4(x + 3)
F) (x - 3)2 = 4(y + 1)
Find the vertex, focus, and directrix of the parabola with the given equation.
19) (y - 2)2 = 8(x + 3)
A) vertex: (- 3, 2)
B) vertex: (- 3, 2)
focus: (- 1, 2)
focus: (- 3, 2)
directrix: x = - 5
directrix: x = - 3
D) vertex: (2, - 3)
E) vertex: (- 3, 2)
focus: (1, - 2)
focus: (- 5, 2)
directrix: x = - 5
directrix: x = - 1
Match the equation to the graph.
20) (y + 2)2 = 5(x - 2)
A)
19)
C) vertex: (3, - 2)
focus: (5, - 2)
directrix: x = 1
F) vertex: (2, - 3)
focus: (4, - 3)
directrix: x = 0
20)
B)
C)
D)
E)
F)
4
1a
2e
3e
4b
5f
6c
7e
8b
9d
10a
11a
12f
13c
14b
15d
16f
17f
18f
19a
20c