Exam 3 Math 1314 Litong Name ____________________________________________ Test No_____________
Find the equation that the given graph represents.
Find the correct end behavior diagram for the given
polynomial function.
4) P(x) = 3x7 + 8x2 - 7
1)
Graph the polynomial function. Factor first if the
expression is not in factored form.
5) f(x) = -2x(x - 1)2
y
5
A) P(x) = x5 + 3x 4 - 5x 3 - 15x2 + x + 10
B) P(x) = -x5 - 5x 3 - 6x 2 + 10x
C) P(x) = -x3 + 15x2 + x - 10
D) P(x) = x4 - 5x 3 + 6x 2 + x + 10
-5
x
5
-5
Solve the problem.
2) The graph of f(x) = x4 + x3 - 6x2 - x2 - x + 6 is
shown below. Use the graph to factor f(x).
6) f(x) = x(x + 2)(x - 2)3
y
y
15
25
-5 -4 -3 -2 -1
1
2
3
4
5 x
-4
-3
-2
-1
1
2
3
4
x
-15
-25
Sketch the graph of the polynomial function.
3) f(x) = (x - 5)3 - 1
Solve the problem.
7) A(x) = -0.015x3 + 1.05x gives the alcohol level
in an average personʹs blood x hrs after
drinking 8 oz of 100-proof whiskey. If the
level exceeds 1.5 units, a person is legally
drunk. Would a person be drunk after 5
hours?
y
10
5
-10
-5
5
10
x
-5
-10
1
Use the graph to answer the question.
8) Find the horizontal and vertical asymptotes of
the rational function graphed below.
Find the horizontal asymptote of the given function.
9 - 8x
13) h(x) = - 7x + 3
y
6
Give the equation of the oblique asymptote, if any.
x2 - 7x + 4
14) f(x) = x + 3
4
2
-6
-4
-2
2
4
6
Sketch the graph of the rational function.
5x
15) f(x) = (x - 1)(x + 5)
x
-2
y
-4
-6
Graph the function.
10
9) f(x) = - 2
x2
x
y
10
Graph the function.
x2 - x - 6
16) f(x) = x + 4
10 x
-10
-10
Answer the question
10) How can the graph of f(x) = 1
+ 6 be
x - 8
1
obtained from the graph of y = ?
x
Solve the problem.
17) If m varies directly as x and y, and m = 24
when x = 6 and y = 9, find m when x = 15 and
y = 8.
Give the domain and range for the rational function. Use
interval notation.
1
11) f(x) = (x + 3)2
18) x varies inversely as v, and x = 30 when v = 6.
Find x when v = 36.
Find any vertical asymptotes.
x - 4
12) f(x) = x2 + 5
19) If f varies jointly as q2 and h, and f = 54 when
q = 3 and h = 2, find f when q = 2 and h = 6.
2
Determine whether or not the function is one -to-one.
26) f(x) = 9 - x2
20) If y varies directly as x2 and inversely as m,
and y = 9 when x = 3 and m = 5, find y when x
= 4 and m = 10.
Decide whether or not the functions are inverses of each
other.
27)
21) The weight of a liquid varies directly as its
volume V. If the weight of the liquid in a
cubical container 4 cm on a side is 192 g, find
the weight of the liquid in a cubical container 5
cm on a side.
y
10
22) The time it takes to complete a certain job
varies inversely to the number of people
working on that job. If it takes 32 hours for 7
carpenters to frame a house, then how long
will it take 56 carpenters to do the same job?
-10
10
x
-10
23) The volume V of a given mass of gas varies
directly as the temperature T and inversely as
the pressure P. If V = 140.0 in 3 when T = 100°
and P = 10 lb/in2 , what is the volume when T
= 310° and P = 15 lb/in2 ?
28) f(x) = 8x2 + 8, domain [0, ∞); g(x) = x - 8
,
8
domain [8, ∞)
Answer the question.
24) How many real zeros does this graph have?
If the following defines a one-to-one function, find its
inverse. If not, write ʺNot one-to-one.ʺ
29) {(-3, 12), (14, 12), (8, -10)}
If f is one-to-one, find an equation for its inverse.
30) f(x) = 3x3 - 4
Find the domain and range of the inverse of the given
function.
31) f(x) = 9 - x2 ; x ≥ 0
Determine whether or not the function is one -to-one.
25)
Use the graph of f to sketch a graph of the inverse of f
using a dashed curve.
32)
y
10
y
10
-10
10
5
x
-10
-10
-5
5
-5
-10
3
10 x
8=3
Find the function value. If the result is irrational, round
your answer to the nearest thousandth.
1 x
33) Let f(x) = . Find f(-3).
3
44) log
Graph the function.
34) f(x) = 4 -x
46) log5 x = -2
6
x
45) x = 4 log4 11
y
Graph the function.
47) f(x) = log x
4
4
6
y
2
4
-6
-4
-2
2
4
6 x
2
-2
-4
-6
-4
-2
2
4
6 x
-2
-6
-4
Solve the equation.
-6
1
35) 2 (5 - 3x) = 16
Write the expression as a sum, difference, or product of
logarithms. Assume that all variables represent positive
real numbers.
x5 y 3
48) log3 3
1 x + 2
36) ex - 1 = e4
Evaluate the logarithm.
1
37) log
9 81
38) log
39) log
40) log
10
2
10
Use the product, quotient, and power rules of logarithms
to rewrite the expression as a single logarithm. Assume
that all variables represent positive real numbers.
49) 6 loga q - loga r
1
Given log
2 = 0.3010 and log 3 = 0.4771, find the
10
10
logarithm without using a calculator.
50) log
18
10
2
1,000,000
Use a calculator to find the logarithm. Give an
approximation to four decimal places.
51) log .00320
Write in logarithmic form.
41) 4 3/2 = 8
Write an equivalent expression in exponential form.
1
42) log = -2
2 4
52) ln 300
Use the change of base rule to find the logarithm to four
decimal places.
53) log 0.287
4
Solve the equation.
1
43) log9 = x
729
4
Solve the equation. If necessary, round to the nearest
thousandth.
54) 4 x = 18
55) 5 x+7 = 8 x
Solve the equation and express the solution in exact form.
56) ln(18x + 3) = ln 11
57) ln(6x - 5) + ln (x - 1) = ln 5
Solve the equation.
58) ln ex - ln e7 = ln e8
Solve for the indicated variable.
59) i = v - k ln t , for t
Solve the problem.
60) How long must $4700 be in a bank at 5%
compounded annually to become $6944.04?
(Round to the nearest year.)
5
Answer Key
Testname: MA1314X3REVIEW
1) A
2) f(x) = (x + 3)(x + 1)(x - 1)(x - 2)
3)
y
10
5
-10
-5
5
10
x
-5
-10
4)
5)
y
5
-5
x
5
-5
6)
y
25
-4
-3
-2
-1
1
2
3
4
x
-25
7) Yes
8) Horizontal: y = -1; vertical: x = ±2
6
Answer Key
Testname: MA1314X3REVIEW
9)
y
10
10 x
-10
-10
10) By making a horizontal shift of 8 units to the right and a vertical shift of 6 units up
11) Domain: (-∞, -3) ∪ (-3, ∞); Range: (0, ∞)
12) None
8
13) y = 7
14) y = x - 10
15)
20
16
12
y
8
4
-10 -8 -6 -4 -2
-4
-8
-12
2
4
6 8 10 x
-16
-20
16)
20
10
-20
-10
10
20
-10
-20
17)
160
3
18) 5
19) 72
20) 8
21) 375 g
7
Answer Key
Testname: MA1314X3REVIEW
22) 4.0 hours
23) 289.3 in 3
24) 2
25) Yes
26) No
27) Yes
28) Yes
29) Not one-to-one
3 x + 4
30) f-1 (x) = 3
31) Domain: (-∞, 9]; range: range: [0, ∞)
32)
y
10
5
-10
-5
5
10 x
-5
-10
33) 27
34)
6
y
4
2
-6
-4
-2
2
4
6 x
-2
-4
-6
35) {3}
36) - 7
5
37) -2
38) 0
1
39)
2
40) 6
3
41) log 8 = 4
2
8
Answer Key
Testname: MA1314X3REVIEW
42) 2 -2 = 1
4
43) {-3}
44) {2}
45) 11
1
46)
25
47)
6
y
4
2
-6
-4
-2
2
4
6 x
-2
-4
-6
48) 5 log3 x + 3 log3 y - log3 3
49) loga q6
r
50) 1.2552
51) -2.4949
52) 5.7038
53) -0.9004
54) {2.085}
55) {23.970}
4
56)
9
57)
11
6
58) {15}
59) t = e (v - i)/k
60) 8 yr
9