Practice problems for exam 3 v2
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School
University of Missouri, Columbia *
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Course
1100
Subject
Mathematics
Date
Jan 9, 2024
Type
Pages
8
Uploaded by PrivateDangerNightingale23
1.
2.
3.
4.
5.
6.
Convert to a logarithmic equation.
b
a
= 21
The equation is .
(Use integers or fractions for any numbers in the equation.)
Solve for x.
2
8x
= 8
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A.
The solution is x
.
=
(Simplify your answer. Type an integer or a fraction. Use a comma to separate answers as needed.)
B.
The solution is not a real number.
Solve the following inequality.
x
− 14x + 45 > 0
2
The solution is .
(Type your answer in interval notation. Use integers or fractions for any numbers in the expression. Type an exact answer, using radicals as needed.)
Solve for x.
ln
x = 7
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A.
The solution is x
.
=
(Type an exact answer in simplified form. Type exponential notation with positive exponents. Use a comma to separate answers as needed.)
B.
The solution is not a real number.
Find the graph that matches the given system of equations.
x = − 3y
x
y
−
= − 8
A.
-12 -6
6
12
-12
-6
6
12
x
y
B.
-12 -6
6
12
-12
-6
6
12
x
y
C.
-12 -6
6
12
-12
-6
6
12
x
y
D.
-12 -6
6
12
-12
-6
6
12
x
y
Find the vertical asymptote(s) of the graph of the given function. f(x) =
x − 8
x
2
+ 9x
A.
x
0, x
=
= 9
B.
x = 8
C.
x = − 9
D.
x
0, x
=
= − 9
7.
8.
9.
10.
11.
Find the inverse of the relation.
{(
, ), ( , ), ( , ), (5, 5)}
− 9
− 8
6 7
8 9
−
The inverse is {
}.
(Type ordered pairs, separated by commas.)
Solve using the substitution method.
3x − 7y = 13
4x + 41
y
=
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A.
The solution of the system is .
(Type an ordered pair.)
B.
There are infinitely many solutions in the form .
x,
C.
There is no solution.
Solve the following system of equations.
4x + 7y
= 7
8x
+ 2z
= 4
6y
+ 2z
= 10
Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice.
A.
There is one solution. The solution is .
,
,
(Type integers or simplified fractions.)
B.
There are infinitely many solutions. The solutions are .
,
,z
(Type integers or simplified fractions.)
C.
There is no solution.
Express as a sum of logarithms.
yz
log
x
3
A.
(
)(
y)(
z)
log
x
3
log
x
log
x
B.
y
z
log
x
3 +
log
x
+
log
x
C.
(
y
z)
log
x
3 +
+
D.
y
z
log
3
+
log
3
Determine whether the function is one-to-one. If it is, find a formula for its inverse.
f(x) =
8
x + 4
Is the function one-to-one?
Yes
No
What is the inverse function? Select the correct choice below and fill in the answer box within your choice if necessary.
A.
(x)
f
− 1
=
B.
The function is not one-to-one.
12.
13.
14.
15.
16.
Match the inequality with a graph.
x
y
8
− 7
≥ − 5
A.
-12 -6
6
12
-12
-6
6
12
x
y
B.
-12 -6
6
12
-12
-6
6
12
x
y
C.
-12 -6
6
12
-12
-6
6
12
x
y
D.
-12 -6
6
12
-12
-6
6
12
x
y
For the function g(x)
, solve the following inequality.
=
x + 7
x − 6
g(x)
0
>
Select the correct choice below and fill in the answer box within your choice.
A.
The solution is . (Simplify your answer. Type your answer in interval notation.)
B.
The solution is . (Simplify your answer. Use a comma to separate answers as needed.)
Graph the inequality.
x
y
3
− 4
≤ − 16
Use the graphing tool on the right to graph the inequality.
-10
-8
-6
-4
-2
2
4
6
8
10
-10
-8
-6
-4
-2
2
4
6
8
10
x
y
Find the logarithm.
log
36
6
log
36
6
=
Determine the horizontal asymptote of the graph of the function.
f(x) =
x
3
− 3x
2
+ x − 4
x
2
− 18
Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A.
The horizontal asymptote is y
.
=
(Type an integer or a fraction.)
B.
There is no horizontal asymptote.
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17.
18.
19.
20.
Use a calculator to find the value to the nearest ten-thousandth.
e
− 3.44
e
− 3.44
=
(Round to four decimal places as needed.)
Solve the following logarithmic equation.
log
(c + 27)
2
−
log
(c + 7)
2
=
log
c
2
Select the correct choice below and, if necessary, fill in the answer box.
A.
The solution(s) is/are .
(Simplify your answer. Type an integer or a fraction. Use a comma to separate answers as needed.)
B.
The solution is not a real number.
List all the asymptotes of the following function.
R(x) =
9
x
2
− 16
What is/are the equation(s) of the vertical asymptote(s) of R(x)? Select the correct choice and, if necessary, fill in the answer box to complete your choice.
A.
The vertical asymptote(s) is/are .
(Use a comma to separate answers as needed. Type an equation(s).)
B.
There is no vertical asymptote.
What is the equation of the horizontal asymptote of R(x)? Select the correct choice and, if necessary, fill in the answer box to complete your choice.
A.
The horizontal asymptote is . (Type an equation.)
B.
There is no horizontal asymptote.
Graph the system of inequalities. Then find the coordinates of the vertices.
x
y
+
≤ 2
x
y
−
≤ 6
Use the graphing tool to graph the system of inequalities.
The vertex(vertices) is(are) .
(Type an ordered pair. Use a comma to separate answers as needed.)
-10
-8
-6
-4
-2
2
4
6
8
10
-10
-8
-6
-4
-2
2
4
6
8
10
x
y
21.
22.
23.
24.
25.
26.
For the function g(x)
solve the following.
= x
− 4x
5
3
g(x)
0
>
Select the correct choice below and fill in the answer box within your choice.
A.
The solution is . (Type your answer in interval notation.)
B.
The solution is . (Use a comma to separate answers as needed.)
Determine the domain of the function. f(x) =
3x − 5
3x + 36
The domain is . (Type your answer in interval notation.)
Express as the sum or difference of logarithms.
log
5z
6
log
5z
6
=
(Simplify your answer.)
Express in terms of sums and differences of logarithms.
ln
9
8x
8
y
ln
9
8x
8
y
=
Convert to an exponential equation.
log
T
n
= − z
The equivalent equation is .
(Type in exponential form.)
A one-cup serving of spaghetti with meatballs contains 260 calories and 32 grams of carbohydrates. A one-cup serving of chopped iceberg lettuce contains 5 calories and 1 gram of carbohydrates. Determine how many servings of each would be required to obtain calories and grams of carbohydrates.
240
30
How many serving(s) of spaghetti would be required? (Round to the nearest tenth.)
How many serving(s) of iceberg lettuce would be required? (Round to the nearest tenth.)
1.
log
21 = a
b
2.
A. The solution is x
.
=
3
8
(Simplify your answer. Type an integer or a fraction. Use a comma to separate answers as needed.)
3. ( −
,5)
(9,
)
4.
A. The solution is x
.
=
7
(Type an exact answer in simplified form. Type exponential notation with positive exponents. Use a comma to separate answers as needed.)
5.
B. -12 -6
6
12
-12
-6
6
12
x
y
6. D. x
0, x
=
= − 9
7. ( − 8, − 9),(7,6),(9,8),( − 5,5)
8.
A. The solution of the system is .
( − 12, − 7)
(Type an ordered pair.)
9. A. There is one solution. The solution is .
0
,
1
,
2
(Type integers or simplified fractions.)
10. B. y
z
log
x
3 +
log
x
+
log
x
11. Yes
A. (x)
f
− 1
=
− 4
8
x
12.
B. -12 -6
6
12
-12
-6
6
12
x
y
13.
A. The solution is . ( −
, − 7)
(6,
)
(Simplify your answer. Type your answer in interval notation.)
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14.
-10
-8
-6
-4
-2
2
4
6
8
10
-10
-8
-6
-4
-2
2
4
6
8
10
x
y
15. 2
16. B. There is no horizontal asymptote.
17. 0.0321
18.
A. The solution(s) is/are .
3
(Simplify your answer. Type an integer or a fraction. Use a comma to separate answers as needed.)
19.
A. The vertical asymptote(s) is/are .
x = − 4,x = 4
(Use a comma to separate answers as needed. Type an equation(s).)
A. The horizontal asymptote is . (Type an equation.)
y = 0
20.
-10
-8
-6
-4
-2
2
4
6
8
10
-10
-8
-6
-4
-2
2
4
6
8
10
x
y
(4, − 2)
21.
A. The solution is . (Type your answer in interval notation.)
( − 2,0)
(2,
)
22. ( −
, − 12)
( − 12,
)
23.
log
5 +
log
z
6
6
24.
ln
9 −
ln
8 − 8
ln
x −
ln
y
25.
n
= T
− z
26. 0.9
1.2