MTH 112 - Practice Test 2
Sections 2.4, 2.5, 2.6, 2.7, 1.8, 3.1, and 3.2
Divide using long division.
1)
8x3
+
18x2
+
13x
+
5
-
4x
-
3
Find an nth degree polynomial function with real coefficients satisfying the given conditions.
13) n
=
3; 3 and i are zeros; f(2)
=
30
2)
x4
-
2x3
-
7x2
+
4x
+
12 x2
-
3x
-
2
Factor the polynomial as the product of factors that are irreducible over the real numbers. Then write the polynomial in completely factored form involving complex nonreal, or imaginary numbers.
14) f(x)
=
x4
+
2x3
-
4x2
+
8x
-
32 (Hint: x2
+
4 is a factor.)
3)
8b4
+
12b3
-
2b
2b2
+
b
Divide using synthetic division.
4) (x2
+
8x
+
9) ÷ (x
+
5)
Find all zeros of the function and write the polynomial as a product of linear factors.
15) f(x)
=
2x4
-
5x3
+
10x2
-
20x
+
8
5)
5x3
-
7x2
-
8x
+
4 x
-
2
Find the domain of the rational function.
16) f(x)
= x
+ x2
-
4
25
6) x5
+
x3
-
5 x
-
2
17) f(x)
= x
+
2 x2
+
9
Use synthetic division and the Remainder Theorem to find the indicated function value.
7) f(x)
=
4x3
-
8x2
-
4x
+
23; f(
-
3)
Find the vertical asymptotes, if any, of the graph of the rational function.
18) h(x)
= x x(x
+
3) Solve the problem.
8) Solve the equation 3x3
-
29x2
+
78x
-
40
=
0 given that 4 is a zero of f(x)
=
3x3
-
29x2
+
78x
-
40.
19) f(x)
= x x2
+
4
Use the Rational Zero Theorem to list all possible rational zeros for the given function.
9) f(x)
=
6x4
+
4x3
-
2x2
+
2
20) x
-
25 x2
-
8x
+
15
Find a rational zero of the polynomial function and use it to find all the zeros of the function.
10) f(x)
=
x4
+
5x3
-
2x2
-
18x
-
12
Find the horizontal asymptote, if any, of the graph of the rational function.
21) g(x)
=
6x2
2x2
+
1
11) f(x)
=
x4
-
3x3
+
19x2
+
53x
-
174
22) h(x)
=
25x3
5x2
+
1
12) f(x)
=
x3
+
6x2
-
x
-
6
23) f(x)
=
15x
3x2
+
1
1

Graph the rational function.
24) f(x)
=
2x
-
9 x
-
5
Graph the rational function.
25) f(x)
= x2 x2
-
x
-
56
Find the indicated intercept(s) of the graph of the function.
26) x
intercepts of f(x)
= x
-
6 x2
+
5x
-
2
27) x
intercepts of f(x)
= x2
+
3 x2
+
6x
+
4
28) y
intercept of f(x)
= x2
-
5 x2
+
11x
-
5
29) y
intercept of f(x)
= x2
-
7x
+
3
2x
2
Find the slant asymptote, if any, of the graph of the rational function.
30) f(x)
= x2
+
6x
-
8 x
-
7
31) f(x)
=
6x2
5x2
+
3
Given the graph of f(x), solve f(x)
≥
0.
32)
-10 -8 -6 -4 -2 2 4 6 8 10
Given the graph of f(x), solve f(x)
<
0.
33)

Solve the polynomial inequality and graph the solution set on a number line. Please show signs(
+
or
-
) in each interval. Express the solution set in interval notation.
34) 2x2
-
5x
≥
7
42) f(x)
=
(x
+
2)3
43) f(x)
=
x
+
4
Does the graph represent a function that has an inverse function?
44)
35) x
<
42
-
x2
36) 9x2
-
2x
≤
0
Solve the rational inequality and graph the solution set on a real number line. Express the solution set in interval notation.
37)
16
-
4x
5x
+
8
≤
0
45)
A) Yes B) No
38) x
-
2 x
+
1
<
0
39)
2x x
+
5
<
x
Find the inverse of the one
to
one function.
40) f(x)
=
3
8x
-
5
41) f(x)
=
8x
+
4
46)
A) Yes
A) Yes
B) No
B) No
3

Use the graph of f to draw the graph of its inverse function.
47)
Graph the function by making a table of coordinates.
50) f(x)
=
5x
48)
51) f(x)
=
0.6x
Graph f as a solid line and f -
1 as a dashed line in the same rectangular coordinate space. Use interval notation to give the domain and range of f and f -
1.
49) f(x)
=
3 x
+
3
52) g(x)
=
ex
-
3.
-10 -8 -6 -4 -2 2 4 6 8
-8 -6 -4 -2
4

Approximate the number using a calculator. Round your answer to three decimal places.
53) e -
0.6
Use the compound interest formulas A
=
P 1
+ r n nt
and
A
=
Pert to solve.
54) Find the accumulated value of an investment of $7000 at 7% compounded continuously for 6 years.
55) Find the accumulated value of an investment of $800 at 10% compounded quarterly for 5 years.
Write the equation in its equivalent exponential form.
56) log b
9
=
2
Write the equation in its equivalent logarithmic form.
57) 63
=
x
Graph the function.
58) g(x)
= log3x
Evaluate the expression without using a calculator.
62) log3 243
63) log
5
1
64) log
9
9
65) log
2
211
66) log
67) eln 242
68) ln
69) ln e
4
100 e
1
70) 8 log 103.9
Find the domain of the logarithmic function.
59) f(x)
=
log
5
(x
-
5)
Evaluate the expression without using a calculator.
1
60) log
2 8
61) 10log 6
A) 6
C) 1,000,000
B) 60
D) 0.000001
5

Answer Key
Testname: MTH 112 PRACTICETEST2
1)
-
2x2
-
3x
-
1
+
2
-
4x
-
3
2) x2
+
x
-
2
+
8 x2
-
3x
-
2
3) 4b2
+
4b
-
2
4) x
+
3
-
6 x
+
5
5) 5x2
+
3x
-
2
6) x4
+
2x3
+
5x2
+
10x
+
20
+
35 x
-
2
7)
-
145
8) 4, 5,
2
3
9) ±
1
6
, ±
1
3
, ±
1
2
, ±
2
3
, ± 1, ± 2
10) {
-
1, 2,
-
3
+
3,
-
3
-
3}
11) {
-
3, 2, 2
+
5i, 2
-
5i}
12) {1,
-
1,
-
6}
13) f(x)
= -
6x3
+
18x2
-
6x
+
18
14) f(x)
=
(x
+
4)(x
-
2)(x
-
2i)(x
+
2i)
15) f(x)
=
(2x
-
1)(x
-
2)(x
+
2i)(x
-
2i)
16) (
-∞
,
-
5)
∪
(
-
5,5)
∪
(5,
∞
)
17) (
-∞
,
∞
)
18) x
= -
3
19) no vertical asymptote
20) x
=
5, x
=
3
21) y
=
3
22) no horizontal asymptote
23) y
=
0
24)
25)
26) (6, 0)
27) none
28) 0, 1
29) none
30) y
=
x
+
13
31) no slant asymptote
32) (
-∞
,
-
2]
∪
[2,
∞
)
33) (
-∞
,
-
1)
∪
(0, 1)
34) (
-∞
,
-
1]
∪
7
2
,
∞
35) (
-
7, 6)
36) 0,
2
9
6
37)
-∞
,
-
8
5
or [4,
∞
)
38) (
-
1, 2)
39) (
-
5,
-
3)
∪
(0,
∞
)
40) f 1(x)
=
3
8x
+
5
8
41) f 1(x)
= x
-
4
8
42) f 1(x)
=
3 x
-
2
43) f -
1(x)
=
x2
-
4
44) B

Answer Key
Testname: MTH 112 PRACTICETEST2
45) A
46) B
47)
50)
51)
48)
52)
49)
-10 -8 -6 -4 -2 2 4 6 8 f domain
=
(
-∞
,
∞
); range
=
(
-∞
,
∞
) f -
1 domain
=
(
-∞
,
∞
); range
=
(
-∞
,
∞
)
7
-6 -4 -2
53) 0.549
54) $10,653.73
55) $1310.89
56) b2
=
9
57) log
6
x
=
3

Answer Key
Testname: MTH 112 PRACTICETEST2
58)
59) (5,
∞
)
60)
-
3
61) A
62) 5
63) 0
64) 1
65) 11
66)
-
2
67) 242
68)
1
4
69) 1
70) 31.2
8