Download MTH 112 practicetest2.tst

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.
8x3 + 18x2 + 13x + 5
1)
-4x - 3
2)
x4 - 2x3 - 7x2 + 4x + 12
x2 - 3x - 2
3)
8b4 + 12b3 - 2b
2b2 + b
Find an nth degree polynomial function with real
coefficients satisfying the given conditions.
13) n = 3; 3 and i are zeros; f(2) = 30
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.)
Find all zeros of the function and write the polynomial as
a product of linear factors.
15) f(x) = 2x4 - 5x3 + 10x2 - 20x + 8
Divide using synthetic division.
4) (x2 + 8x + 9) ÷ (x + 5)
5)
5x3 - 7x2 - 8x + 4
x-2
6)
x5 + x3 - 5
x-2
Find the domain of the rational function.
x+4
16) f(x) =
x2 - 25
17) f(x) =
Use synthetic division and the Remainder Theorem to find
the indicated function value.
7) f(x) = 4x3 - 8x2 - 4x + 23; f(-3)
x+2
x2 + 9
Find the vertical asymptotes, if any, of the graph of the
rational function.
x
18) h(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) =
Use the Rational Zero Theorem to list all possible rational
zeros for the given function.
9) f(x) = 6x4 + 4x3 - 2x2 + 2
20)
x
2
x +4
x - 25
x2 - 8x + 15
Find the horizontal asymptote, if any, of the graph of the
rational function.
6x2
21) g(x) =
2x2 + 1
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
11) f(x) = x4 - 3x3 + 19x2 + 53x - 174
22) h(x) =
25x3
5x2 + 1
23) f(x) =
15x
3x2 + 1
12) f(x) = x3 + 6x2 - x - 6
1
Graph the rational function.
2x - 9
24) f(x) =
x-5
Find the slant asymptote, if any, of the graph of the
rational function.
x2 + 6x - 8
30) f(x) =
x-7
y
31) f(x) =
5
-10
-5
5
6x2
5x2 + 3
Given the graph of f(x), solve f(x) ≥ 0.
32)
10 x
y
20
-5
16
12
8
4
Graph the rational function.
x2
25) f(x) =
x2 - x - 56
-10 -8
-6
-4
-2
-4
2
4
6
8
10
-8
-12
-16
y
-20
5
Given the graph of f(x), solve f(x) < 0.
33)
y
-10
-5
5
10 x
5
-5
-5
Find the indicated intercept(s) of the graph of the function.
x-6
26) x-intercepts of f(x) =
x2 + 5x - 2
27) x-intercepts of f(x) =
28) y-intercept of f(x) =
29) y-intercept of f(x) =
5
-5
x2 + 3
x2 + 6x + 4
x2 - 5
x2 + 11x - 5
x2 - 7x + 3
2x
2
x
x
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)
y
35) x < 42 - x2
x
36) 9x2 - 2x ≤ 0
A) Yes
Solve the rational inequality and graph the solution set on
a real number line. Express the solution set in interval
notation.
16 - 4x
37)
≤0
5x + 8
B) No
45)
y
x
38)
x-2
<0
x+1
A) Yes
B) No
46)
y
2x
39)
<x
x+5
x
Find the inverse of the one-to-one function.
3
40) f(x) =
8x - 5
A) Yes
41) f(x) = 8x + 4
3
B) No
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) = 5 x
y
8
y
10
6
5
4
2
-10
-5
5
10
x
-8
-6
-4
-2
2
-5
4
8x
6
-2
-4
-10
-6
-8
48)
y
10
51) f(x) = 0.6 x
5
y
6
-10
-5
5
10
x
4
-5
2
-10
-6
-4
-2
2
4
x
6
-2
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
-4
-6
x+3
10
y
52) g(x) = ex - 3.
8
6
y
4
6
2
-10 -8
-6
-4
-2
4
2
4
6
8
x
2
-2
-4
-8
-6
-4
-2
2
-6
-2
-8
-4
-10
-6
4
4
6
8
x
Approximate the number using a calculator. Round your
answer to three decimal places.
53) e-0.6
Evaluate the expression without using a calculator.
62) log3 243
63) log 1
5
r nt
Use the compound interest formulas A = P 1 +
and
n
64) log 9
9
A = Pe rt to solve.
54) Find the accumulated value of an investment
of $7000 at 7% compounded continuously for 6
years.
65) log 2 11
2
55) Find the accumulated value of an investment
of $800 at 10% compounded quarterly for 5
years.
66) log
Write the equation in its equivalent exponential form.
56) log 9 = 2
b
67) eln 242
Write the equation in its equivalent logarithmic form.
57) 6 3 = x
68) ln
4
e
69) ln e
Graph the function.
58) g(x) =log3 x
70) 8 log 103.9
y
6
-6
6
x
-6
Find the domain of the logarithmic function.
59) f(x) = log (x - 5)
5
Evaluate the expression without using a calculator.
1
60) log
2 8
61) 10log 6
A) 6
C) 1,000,000
1
100
B) 60
D) 0.000001
5
Answer Key
Testname: MTH 112 PRACTICETEST2
1) -2x2 - 3x - 1 +
2) x2 + x - 2 +
2
-4x - 3
25)
y
8
6
x2 - 3x - 2
5
4
3) 4b2 + 4b - 2
6
4) x + 3 x+5
3
2
1
5) 5x2 + 3x - 2
-16
6) x4 + 2x3 + 5x2 + 10x + 20 +
-8
35
x-2
-1
-2
-3
7) -145
-4
2
8) 4, 5,
3
-5
9) ±
-6
1
1
1
2
, ± , ± , ± , ± 1, ± 2
6
3
2
3
26) (6, 0)
27) none
28) 0, 1
29) none
30) y = x + 13
31) no slant asymptote
32) (-∞,-2] ∪ [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)
33) (-∞, -1) ∪ (0, 1)
34) (-∞, -1] ∪
7
,∞
2
35) (-7, 6)
36) 0,
2
9
y
10
37) -∞, -
5
-10
-5
5
10
8
or [4, ∞)
5
38) (-1, 2)
x
39) (-5, -3) ∪ (0, ∞)
-5
40) f-1 (x) =
-10
3
5
+
8x 8
x-4
41) f-1 (x) =
8
3
42) f-1 (x) = x - 2
43) f-1 (x) = x2 - 4
44) B
6
8
16
x
Answer Key
Testname: MTH 112 PRACTICETEST2
45) A
46) B
47)
50)
6
y
y
4
10
2
5
-6
-4
-2
2
4
6 x
2
4
6 x
-2
-10
-5
5
10
x
-4
-5
-6
51)
-10
48)
6
y
y
10
4
2
5
-6
-10
-5
5
10
-4
-2
x
-2
-4
-5
-6
-10
52)
49)
y
10
y
6
8
4
6
2
4
2
-6
-4
-2
2
-2
-10 -8
-6
-4
-2
2
4
6
8
x
-2
-4
-4
-6
-6
53) 0.549
54) $10,653.73
55) $1310.89
56) b2 = 9
-8
-10
f domain = (-∞, ∞); range = (-∞, ∞)
f -1 domain = (-∞, ∞); range = (-∞, ∞)
57) log
7
6
x=3
4
6
x
Answer Key
Testname: MTH 112 PRACTICETEST2
58)
y
6
-6
6
x
-6
59) (5, ∞)
60) -3
61) A
62) 5
63) 0
64) 1
65) 11
66) -2
67) 242
1
68)
4
69) 1
70) 31.2
8