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Test 3
Math 1314
Name___________________________________
Write the domain in interval notation.
x2 - 9
1) f (x) =
x+3
Use the product property of logarithms to write
the logarithm as a sum of logarithms. Then
simplify if possible.
9) log (abc)
1/8
2) f (x) =
19x
Write the equation in logarithmic form.
10) 34 = 81
x2 + 144
Determine the vertical asymptote(s) of the graph
of the function.
x
3) f (x) =
2
x + 16
4) f (a) =
Graph the function.
4
11) p(x) =
2
x - 36
Solve the inequality. Write the solution set in
interval notation.
12) 4x2 - 19x - 5 0
a2 + 36
a2 - 5a - 8
a. Identify the horizontal asymptote (if any).
b. If the graph of the function has a horizontal
asymptote, determine the point where the graph
crosses the horizontal asymptote.
2x - 10
5) s(x) =
2
x + 7x - 4
6) f (x) =
13)
x2
x2 + 49
0
Determine if the relation defines y as a one-to-one
function of x.
14)
x2 + 8x2 - 8
3x - 7
Identify the asymptotes.
-3x2 + 5
7) f (x) =
x
Solve the inequality. Write the solution set in
interval notation.
8) (x + 3)(x + 5) -1
1
A one-to-one function is given. Write an
expression for the inverse function.
23) f (x) = 5x3 - 7.
Write as the sum or difference of logarithms and
fully simplify, if possible. Assume the variable
represents a positive real number.
4
15) log
ab
Write the logarithmic expression as a single
logarithm with coefficient 1, and simplify as much
as possible.
24) log5 10 + log5 20 - log5 8
c8
Write the logarithm as a sum or difference of
logarithms. Simplify each term as much as
possible.
16) log x4 y7
Solve the equation.
25) 32x+4 = 26x
8
A relation in x and y is given. Determine if the
relation defines y as a one-to-one function of x.
17) {(-6, 1), -7, 1), (-2, 2), (4, -4)}
26)
16 = 4t
Solve the equation. Write the solution set with the
exact solutions. Also give approximate solutions to
4 decimal places if necessary.
27) log (x2 - 2x) = log 35
A one-to-one function is given. Write an
expression for the inverse function.
9-x
18) f (x) =
5
Solve the logarithmic equation.
28) log x = 1 - log(x + 3)
Simplify the expression.
19) log 32
1/2
Solve the equation. Write the solution set with the
exact solutions. Also give approximate solutions to
4 decimal places if necessary.
29) log(p + 4) = 4.1
Write the equation in exponential form.
1
= -3
20) log
4 64
Solve the equation.
30) log (-x) + log (x - 20) = log 96
A one-to-one function is given. Write an
expression for the inverse function.
x+5
21) f (x) =
x-1
8
8
8
Determine whether the ordered pair is a solution
of the system.
31) (-2, 6);
5x - 9y = -64
-2x + 8y = 52
Write the logarithmic expression as a single
logarithm with coefficient 1, and simplify as much
as possible.
22) 3log m - 4log n
2
4
Solve the system by substitution.
y = -3x - 7
32)
-4x - 7y = 15
2
2
Solve the system of equations by using the addition
method.
40) 5x - 3y = -19
4x + 5y = 7
Solve the system by using any method. If a system
does not have one unique solution, state whether
the system is inconsistent or whether the equations
are dependent.
2
33) y = x + 1
7
Evaluate the determinant of the given matrix.
5
6
5
41) A = 7
7y - 2x = 7
34) 6x + y = -6
-12x - 2y = 4
25
Solve the system of equations by using the
substitution method.
35) y = x2 + 4
7x - y = 6
42) A =
Give the order of the matrix. Classify the matrix
as a square matrix, row matrix, column matrix, or
none of these.
36) -3 5 7 4
Find B - A.
-5
37) A = 4
8
3
5
-3 , B = 9
-8
3
5
1
9
Perform the indicated operations.
38) Find 3A + 5B.
-5
7
-5
4
and B =
-6
2
Find AB, if possible.
9 4
39) A = 5 -1
-1 -1
-6
2
4 and B = 8
5
9
A=
2
-9
2
4
9
0
3
u
7
35
8
u
Answer Key
Testname: REVIEW TEST 3- SUMMER 2016
1) (- , -3) (-3, )
2) (- , )
3) None
5 + 57
5 - 57
and a =
4) a =
2
2
5) a. y = 0
b. (5, 0)
6) a. No horizontal asymptote
b. Not applicable
7) Vertical asymptote: x = 0;
Slant asymptote: y = -3x
8) {-4}
9) log a + log b + log c
1/8
1/8
1/8
10) log 81 = 4
3
11)
12)
,-
1
4
[5, )
13) (- , )
14) No
1
1
15) log a + log b - 8log c
4
4
16) 4log x + 7log y
8
8
17) No
18) f -1(x) = 9 - 5x
19) -5
1
20) 4-3 =
64
4
Answer Key
Testname: REVIEW TEST 3- SUMMER 2016
21) f -1(x) =
22) log
2
5 + 1x
x-1
m3
n4
x+7
23) f -1(x) = 3
5
24) 2
25) {20}
1
26)
2
27) {7, -5}
28) {2}
29) {104.1 - 4}; p 12,585.2541
30) { }
31) Yes
32) {(-2, -1)}
2
33) (x, y) y = x + 1 ; The equations are dependent.
7
34) { }; The system is inconsistent.
35) {(5, 29), (2, 8)}
36) 1×4, row matrix
10
2
37) 5
4
-5 17
26 -5 30
38)
-17 41 -18
-4
39) 38
35
40) {(-2, 3)}
41) -5
42) u2 - 56
5