Lonestar College Algebra Find the Product Question

rejie.ES?::::::-::::::5⑤→sec.1a40uadraticEquationsf9 →sec.%SWordProbkms÷
%fᵗÉ
✗→
strip
of floor
¥ÉH
Root
a
square feet
Area of
Rug
means
=
Width
(Length of rug)(
(28
Ar⇐
”
352
)
of rug
) (22-211)
=
2x
-56×-44×+4×20
616
–
2=-1×2-1%+264
?⃝
✗
=
2-25×+66=0
(x
–
3) Cx -227=0
=
352
352
-352
=
0
}¥×=¥¥
length
of rug
__
=
28-2×1
220ft
28-213)
widthofrug
=
Ch
=
22-26)
=④ft
(22×16)=352✓
224-6–754
④
22-24
=
–
¥4
¥-4K 4)
”
”
#
É¥+4TÉÉÉÉÉD%%nnnxnnq
22=33-12–3-8
¥20
z-0-doesitcheck.IO
2-E-
”
⑤
5*63+1>-3+4
3+4×+19>-3+4×4-1
*”
”
ftp.163.T
④
14×-21+2=7
*
R④
-2
-2
14×-21–5
Then
/
4×-2=5
✗
X=c×É
4×-2=-5
–
c
{¥ ¥ }
X=_
,
/ ✗ / =L,
If
–
,
Bo
⑧ÉDiaMidpit④
,**+yaa
Sec 2.2
→
( circles
h
k
center C- 1,0 ,
④
radius 2
÷¥¥÷;¥¥÷:÷
↳ Sec
?⃝
?⃝
?⃝
2.3
④
:*:÷ +
(-4*-6)
”
1•Ñ••#-
.
domain
”
f4
decreasing
C-×,
–
4)
constant
e
24-2SQSec.2.SK/-quations-fLines
)
sec.2.6-c ommonfund-ims pieceywi.se#y- x2y- 1Hy- Txy- x
26-310
→
}
I
f
F
F
µ
Functions
←
3ÉTafmatiÉt
)
Compositions
ÉÉFÉÉÉ
of functions
④
a)
glx)
f- 1×7=-6×+9
(f-
◦
④
-66×+97+9
=
[7×+90
=
fog
b)
(
9°f④
C_6
-7×+9
-42×-54+9
=
”
linear
”
-42×-4504
domain
=
> (-6×+9)+9
-42×+631-9
g◦f=-42Xdomfib_
=
④
→
se.cz/-
→
Quadratic
Functions
Imran
::÷÷:÷:;::=÷
✓
factored
)
430*-1×1=2×1×-271×+1
①
[
✗
–
ints :
2×-01×-2=01×+1–0)
%
✗
=L
-1
✗=
1%0711-1,0
–
2.06 2) (0+1)
–
y
int : co -0)
,
–
y=
=
01-274 )
✓
②
ends
2*4%-19
g*•_③2×4%-2%+19
↑
•
middle
:*
)
9=24111-214+1
(2)
21 1)
–
y=
us
¥D
¥¥is
.ms?;!:Hsi-;:i-!;:::#-.oy–txx-?
46-9,
0
.mn#.-..H.A.y–0-…-d?T;.Is….H.A
0,91=0
Domain
Range
.
If
v!a
!
VA
.
↳
.
5-8
.
x=0•
on
(Inverse Functions)
48-520 → sec
⑧
:-#
Ftx*=3
of
×¥¥;¥¥
”
y=×3-9
+
Range
t
Domain
f- 4)
fix ) and
‘
“¥¥q¥É
(
*
*
Functions)
Exponential compounded
Pert (
)
continuously
A-
)ⁿᵗ daily
A=p( HE
quarterly etc
annually,
( compounded
monthly
,
>
,
)
④
compounded
a) semiannually
given $8806.54 →
1=-8806.544+-04*2
)
A-
A-
8806.54%02
8 years -→t=8
4%7 F. 04
(n=I•
A=P(ltᵗn)ⁿᵗ
”
P
find A
”
Cfetureaiue
”
interest
=
$12089.490
__
A
)
–
p
$3282.950
$12127.730
÷
:÷÷÷:H”÷÷:
1-
A=Péᵗ
A-
8806.54C
=
=$332
6o →se4•3↳9zg=¥
,y(6=2
1⑤=X
*÷÷÷÷÷¥
(↑÷÷
④ log
Useful )=1ogyX
?⃝
⑥
f#;
:
%
↳aa**b
nsec4ˢc↳sᵗE✗P[¥¥ⁿI%↳
6⑤Sec.4
I
⑥
i
LNeʰ=④
*LNe
VA
¥3s
,
weEEY.
g
g/x–+-2.
o
a8_s ÷¥:¥ᵈ;¥!÷¥÷_
eÑ=72
⑦ y=4e
2.0681-2.0686
y
”
in 2
→
population 5-2
let
④y=4e0•o
years
”
→
?⃝
⑦
⑧ flt)=Lf⑧é°•°4ᵗ f-(f)
+
(a)
f-
at
beginning
f
t=0
101=140005%04
=
140000°
=/ 4000.1
=14④
→
time Lin
→
# of
days)
people
(b) after todays
f- 6
61=1400050.046
f(
f( 61=11012.79
u⑦”w¥:*
Ha*erⁿ
3.7=21 days
f-
(211–1400050.04121)
=
6043.95
6④
🙂
→s&E:¥÷
substitution
8 → secs.2-lx-dc.no/-usetheGaass
Jordan method
use
,
graphing
)
calculator
a
)
5/2/22, 1:32 PM
Review for Math 1314 Final Exam
Instructor: Kim Lane
Course: Math 0314-1314 section 5C28
ONLINE classes (D2L) – SPRING 2022
Student: _____________________
Date: _____________________
Assignment: Review for Math 1314 Final
Exam
1. Multiply.
−8
−2
−8
−2 =
​(Simplify your answer. Type an exact​answer, using radicals as needed. Type your answer in the form a​+ bi​.)
2. Find the product.
(5 + i )(5 − i )(4 + 2 i )
(5 + i )(5 − i )(4 + 2 i ) =
​(Type your answer in the form a + b i .​)
3. Perform the indicated operations and write the result in standard form.
−8+
− 12
40
−8+
− 12
=
40
​(Simplify your answer. Type an exact​answer, using radicals as needed. Use integers or fractions for any numbers in the
expression. Type your answer in the form a + bi​.)
4. Divide.
6+8i
7+4i
6+8i
=
7+4i
​(Simplify your answer. Use integers or fractions for any numbers in the expression. Type your answer in the form a + bi​.)
5. Use the quadratic formula to solve the equation.
2
y − 10y = − 14
The solution set is ​{
​}.
​(Simplify your answer. Type exact​answers, using radicals as needed. Use a comma to separate answers as​needed.)
6. Solve the equation by the square root property.
2
(z + 4) = − 16
The solution set is
.
​(Simplify your answer. Use a comma to separate answers as​needed.)
7. Find all solutions by factoring.
5s2 − 36s = 32
https://xlitemprod.pearsoncmg.com/api/v1/print/highered
The solution set is
.
​(Simplify your answer. Type an integer or a fraction. Use a
comma to separate answers as​needed.)
1/39
5/2/22, 1:32 PM
Review for Math 1314 Final Exam
8. Solve by completing the square.
The solution set is
.
​(Simplify your answer. Type an exact​answer, using radicals
as needed. Use a comma to separate answers as​needed.)
2
x − 14x − 4 = 0
9. Cynthia Besch wants to buy a rug for a room that is 22 ft wide and 28
ft long. She wants to leave a uniform strip of floor around the rug. She
can afford to buy 352 square feet of carpeting. What dimensions
should the rug​have?
22 ft
352 ft
2
28 ft
The dimensions of the rug should be
​(Use a comma to separate answers as​needed.)
ft.
10. A toy manufacturer needs a piece of plastic in the shape of a right triangle with the longer leg 1 cm more than the shorter
leg and the hypotenuse 2 cm more than the shorter leg. How long should the sides of the triangle​be?
The sides are
cm.
​(Use a comma to separate answers as​needed.)
11. Solve the​equation, and check the solutions.
2z
2
z − 16
=
3
z+4
−
2
z−4
Select the correct choice below and fill in any answer boxes in your choice.
A. The solution set is
.
​(Type an integer or a simplified fraction. Use a comma to separate answers as​needed.)
B. The solution set is x|x ≠
.
​(Simplify your answer. Use a comma to separate answers as​needed.)
C. The solution set is ∅.
*12. Solve.
19 − x = x + 1
Select the correct choice​below, and if​necessary, fill in the answer box to complete your choice.
A. The solution set is
.
​(Type an integer or a simplified fraction. Use a comma to separate answers as​needed.)
B. The solution set is ∅.
https://xlitemprod.pearsoncmg.com/api/v1/print/highered
2/39
5/2/22, 1:32 PM
Review for Math 1314 Final Exam
13. Solve and check the given equation with rational exponents.
5/2
x
= 243
Select the correct choice below and, if​necessary, fill in the answer box within your choice.
A. The solution set is
. ​(Use a comma to separate answers as​needed.)
B. There is no solution.
14. Solve the equation.
4
2
4​(x + 2​) − 53(x + 2​) = − 49
The solution set is ​{
​}.
​(Simplify your answer. Use a comma to separate answers as​needed.)
15. Solve the inequality. Write the solution set in interval notation.
3(x + 6) + 1 ≥ 3 + 4x
Write the solution set in interval notation.
16. Solve the inequality.
x−1
x+4
≤0
The solution to the inequality is
​(Type your answer in interval​notation.)
.
17. Solve the equation.
​|4x − 2​| + 2 = 7
Select the correct choice below and, if​necessary, fill in the answer box to complete your choice.
A. The solution set is
.
​(Simplify your answer. Type an integer or a fraction. Use a comma to separate answers as​
needed.)
B. The solution is all real numbers.
C. The solution is the empty set.
18. For the point P(13,17) and Q(18,20)​, find the distance​
d(P,Q) and the coordinates of the midpoint M of the
segment PQ.
What is the​distance?
(​ Simplify your answer. Type an exact​answer, using radicals
as​need.)
What are the coordinates of the midpoint​M?
(​ Simplify your answer. Type an ordered​pair, using integers
or​fractions.)
https://xlitemprod.pearsoncmg.com/api/v1/print/highered
3/39
5/2/22, 1:32 PM
Review for Math 1314 Final Exam
19. Find the​center-radius form of the equation of the circle
described and graph it.
10
y
center ( − 1,0)​, radius 2
Type the​center-radius form of the equation of the circle.
​(Type an equation. Simplify your​answer.)
x
Graph the circle.
-10
10
-10
20. Decide whether the relation defined by the graph to the right
defines a​function, and give the domain and range.
10
y
8
Does the graphed relation define a​function?
6
4
Yes
No
What is the domain of the graphed​relation?
2
-10 -8 -6 -4
-2
-2
x
2
4
6
8 10
-4
-6
​(Type your answer in interval​notation.)
-8
-10
What is the range of the graphed​relation?
​(Type your answer in interval​notation.)
https://xlitemprod.pearsoncmg.com/api/v1/print/highered
4/39
5/2/22, 1:32 PM
Review for Math 1314 Final Exam
21. State the open intervals over which the function is​(a)
increasing,​(b) decreasing, and​(c) constant.
10
8
y
(3,7)
A. The function is increasing over the open​
interval(s)
.
(7,7)
(​ Type your answer in interval notation.
Use a comma to separate answers as​
needed.)
6
4
2
( − 6,0)
-10 -8 -6 -4
-2
-2
x
2
4
6
B. The function is never increasing.
8 10
-4
( − 4, − 6)
(​ a) Select the correct choice below​and, if​necessary, fill in
the answer box to complete your choice.
(​ b) Select the correct choice below​and, if​necessary, fill in
the answer box to complete your choice.
-6
-8
-10
A. The function is decreasing over the
open​interval(s)
.
​(Type your answer in interval notation.
Use a comma to separate answers as​
needed.)
B. The function is never decreasing.
(​ c) Select the correct choice below​and, if​necessary, fill in
the answer box to complete your choice.
A. The function is constant over the open​
interval(s)
.
​(Type your answer in interval notation.
Use a comma to separate answers as​
needed.)
B. The function is never constant.
22. Use the graph to find the indicated value of the function.
​f(3​) =
10
y
8
6
4
2
-10 -8 -6 -4 -2
-2
x
2
4
6
8 10
-4
-6
-8
-10
https://xlitemprod.pearsoncmg.com/api/v1/print/highered
5/39
5/2/22, 1:32 PM
Review for Math 1314 Final Exam
23. Decide whether each relation defines y as a function of x. Give the domain and range.
y=
5
x−3
Does this relation give a​function?
Yes
No
What is the​domain?
​(Type your answer in interval​notation.)
What is the​range?
​(Type your answer in interval​notation.)
24. The graph of a linear function f is shown. a. Identify the​
slope, y-intercept, and​x-intercept.
b. Write the equation that defines f.
10
y
8
6
The slope is
.
​(Type an integer or a simplified​fraction.)
The​y-intercept is
​(Type an ordered​pair.)
.
The​x-intercept is
.
4
2
-10 -8 -6 -4 -2
-2
x
2
4
6
8 10
-4
​(Type an ordered​pair.)
Write equation that defines f.
-6
-8
-10
​f(x) =
25. Write an equation of the line passing through the given point ​( − 3​,6​) and having the given
3
slope m = . Write the final answer in​slope-intercept form.
5
The equation of the line in​slope-intercept form is
.
​(Simplify your answer. Use integers or fractions for any numbers in the​equation.)
https://xlitemprod.pearsoncmg.com/api/v1/print/highered
6/39
5/2/22, 1:32 PM
Review for Math 1314 Final Exam
26. Which one is the graph of ​f(x) = x2 ​? What is its​domain?
2
Which one is the graph of ​f(x) = x ​? Choose the correct graph below.
A.
B.
4
y
C.
5
y
10
x
-2
6
-4
5
-10
y
4
5
-2
H.
6
x
x
-2
G.
5
y
10
-10
F.
y
-4
5
x
-5
4
y
x
-5
E.
D.
y
10
y
x
-5
-4
x
x
5
-4
-5
-10
10
4
-2
-10
What is its​domain?
​(Type your answer in interval​notation.)
27. Which one is the graph of ​f(x) = x ​? On what open interval is it​increasing?
Which one is the graph of ​f(x) = x ​? Choose the correct graph below.
A.
B.
4
y
C.
5
y
10
x
-2
6
-4
5
-10
y
y
5
-5
5
-2
H.
6
x
x
-2
G.
4
y
10
-10
F.
-5
5
x
-5
5
y
x
-5
E.
D.
y
10
x
-4
x
x
4
-4
y
-4
-2
4
-10
10
-10
On what open interval is it​increasing?
​(Type your answer in interval​notation.)
https://xlitemprod.pearsoncmg.com/api/v1/print/highered
7/39
5/2/22, 1:32 PM
Review for Math 1314 Final Exam
28. Which one is the graph of ​f(x) = x3 ​? What is its​range?
3
Which one is the graph of ​?(x) = x ​? Choose the correct graph below.
A.
B.
C.
y
4
y
5
6
x
5
-4
-10
-5
5
10
H.
10
-4
y
6
x
4
5
-2
5
y
x
-2
-5
-5
G.
y
4
x
x
-10
F.
y
y
5
x
-5
E.
y
10
x
-2
D.
-10
-4
x
10
-4
-10
4
-2
What is its​range?
​(Type your answer in interval​notation.)
29.
Which graph is the graph of ​f(x) =
3
x ​? Is there any interval over which the function is​decreasing?
Which of the following is the graph of ​f(x) =
A.
3
B.
5
y
C.
5
y
5
-5
D.
5
x
-5
x ​? Choose the correct graph below.
y
5
x
-5
5
y
x
-5
-5
5
-5
x
-5
5
-5
Is there any interval over which the function is​decreasing?
No
Yes
https://xlitemprod.pearsoncmg.com/api/v1/print/highered
8/39
5/2/22, 1:32 PM
Review for Math 1314 Final Exam
30. Graph the​function, and give its domain and range.
​f(x) =
x+1
Choose the correct graph
A.
B.
12
y
C.
12
y
12
x
-12
12
D.
y
x
-12
-12
12
-12
The range of the function is
​(Type your answer in interval​notation.)
x
-12
12
-12
The domain of the function is
​(Type your answer in interval​notation.)
12
y
x
-12
12
-12
.
.
31. Use the​piecewise-defined function to find the following values for​f(x).
​f(x) =
5 − 2x
if x ≤ 1
2x
if 1 < x < 5 4x + 4 if x ≥ 5 ​f( − 2​) = ​f(1​) = ​f(2​) = ​f(3​) = ​f(5​) = https://xlitemprod.pearsoncmg.com/api/v1/print/highered 9/39 5/2/22, 1:32 PM Review for Math 1314 Final Exam 32. Match each equation in Column I with a description of its graph from Column II as it relates to the graph of y = x2. I ​(a) y = ​(x − 11​)2 ​(b) y = x2 − 11 ​(c) y = 11x2 ​(d) y = ​(x + 11​)2 ​(e) y = x2 + 11 II A. a translation 11 units down B. a translation 11 units to the right C. a translation 11 units up D. a translation 11 units to the left E. a vertical stretching by a factor of 11 Match the equation in Column I with the correct description in Column II. I II (1) 2 ​(a) y = ​(x − 11​) (2) 2 ​(b) y = x − 11 (3) 2 ​(c) y = 11x (4) 2 ​(d) y = ​(x + 11​) (5) 2 ​(e) y = x + 11 (1) C E (2) A D (3) C A (4) B D (5) C B E D E A D C E C E A B B A B D 33. Fill in the blank to correctly complete the following sentence. The graph of ​f(x) = − (1) x is a reflection of the graph of y = x across the (1) x-axis. y-axis. 34. Fill in the blank to correctly complete the following sentence. The graph of ​f(x) = (1) − x is a reflection of the graph of y = x across the (1) x-axis. y-axis. 35. Let ​f(x) = x − ​1, ​h(x) = − x + 3. Find ​(f ◦ ​h)(6​). ​(f ◦ ​h)(6​) = https://xlitemprod.pearsoncmg.com/api/v1/print/highered 10/39 5/2/22, 1:32 PM Review for Math 1314 Final Exam 36. Let ​f(x) = − 3x − ​1, ​h(x) = − x + 3. Find ​(h ◦ ​f)(7​). ​(h ◦ ​f)(7​) = 37. For the functions ​f(x) = − 6x + 9 and ​g(x) = 7x + 9 find the following. (​ a)​(f ◦ ​g)(x) and its domain ​(b)​(g ◦ ​f)(x) and its domain ​(a) ​(f ◦ ​g)(x) = ​(Simplify your​answer.) The domain is . ​(Type your answer in interval​notation.) ​(b)​(g ◦ ​f)(x) = ​(Simplify your​answer.) The domain is . ​(Type your answer in interval​notation.) 38. Let ​f(x) = 4x2 + 4 and ​g(x) = − 2x + 1. Find the following. ​(f − ​g)( − 3​) ​(f − ​g)( − 3​) = 39. Let ​f(x) = x2 − 16 and ​g(x) = 13 − x. Perform the composition or operation indicated. ​(fg)(3​) ​(fg)(3​) = https://xlitemprod.pearsoncmg.com/api/v1/print/highered 11/39 5/2/22, 1:32 PM Review for Math 1314 Final Exam 40. For the given equation and graph of the quadratic​function, do each of the following. Complete parts ​(a) through ​(e). 10 y 8 2 ​f(x) = − 3(x + 8) + 3 6 4 a. Give the domain and range. 2 The domain is . ​(Type your answer in interval​notation.) -10 -8 -6 -4 -2 -2 x 2 4 6 8 10 -4 The range is . ​(Type your answer in interval​notation.) -6 -8 -10 b. Give the coordinates of the vertex. The vertex is ​(Type an ordered​pair.) . c. Give the equation of the axis of symmetry. The axis of symmetry is x = . d. Find the​y-intercept(s). The​y-intercept(s) is/are . (​ Type an ordered pair. Use a comma to separate answers as​needed.) e. Find the​x-intercept(s). The​x-intercept(s) is/are . ​(Type an ordered pair. Use a comma to separate answers as​needed.) 41. Use synthetic division to perform the division. 3 2 3 2 − 8x + 7x − 9x + 5 x−2 − 8x + 7x − 9x + 5 x−2 = ​(Simplify your​answer.) *42. Use synthetic division to find the quotient and the remainder. ​(x3 − 3x2 − 10​) ÷ ​(x + 2​) The quotient is and the remainder is https://xlitemprod.pearsoncmg.com/api/v1/print/highered . 12/39 5/2/22, 1:32 PM Review for Math 1314 Final Exam 43. Graph the function ​f(x) = ​2x(x − 2​)(x + 1​). 50 Use the graphing tool to graph the function. y 40 30 20 10 x -10 -8 -6 -4 -2 -10 2 4 6 8 10 -20 -30 -40 -50 44. Graph the polynomial function. Factor first if the expression is not in factored form. 2 f(x) = x (x − 3)(x + 2) 2 Choose the correct graph below. A. B. 100 y C. 100 y 100 x -6 6 -100 D. y 100 x -6 6 -100 x -6 x 6 -6 -100 6 -100 45. Graph the following polynomial function. 3 y 40 2 ​f(x) = x + 4x − x − 4 32 Use the graphing tool to graph the function. 24 y 16 8 x -10 -8 -6 -4 -2 2 4 6 8 10 -8 -16 -24 -32 -40 https://xlitemprod.pearsoncmg.com/api/v1/print/highered 13/39 5/2/22, 1:32 PM 46. What are the equations of the vertical and the horizontal asymptotes of the graph of y = The vertical asymptote is The horizontal asymptote is 47. Review for Math 1314 Final Exam The horizontal asymptote is x−2 + 3​? . ​(Type an​equation.) . ​(Type an​equation.) What are the equations of the vertical and the horizontal asymptotes of the graph of y = The vertical asymptote is 1 1 (x + 3)2 − 6​? . ​(Type an​equation.) . ​(Type an​equation.) 48. If the function defined by the following is​one-to-one, find its inverse. ​{( − 2​, 6​), ​(2​, 1​), ​(5​, 9​)} Select the correct choice​below, and fill in the answer box if necessary. A. The inverse function is ​{ ​}. ​(Type ordered pairs. Use a comma to separate answers as​needed.) B. The function is not​one-to-one. https://xlitemprod.pearsoncmg.com/api/v1/print/highered 14/39 5/2/22, 1:32 PM Review for Math 1314 Final Exam 49. For the function ​f(x) = 3x − 8​, determine whether​f(x) is​one-to-one. If​so, ​(a) write an equation for the inverse function in the −1 form y = f (x)​, ​(b) graph f and f is not​one-to-one, say so. −1 on the same​axes, and ​(c) give the domain and the range of f and f (​ a) Write an equation for the inverse function in the form y = f any answer boxes to complete your choice. A. The function​f(x) is​one-to-one and f −1 −1 −1 . If the function (x). Select the correct choice below​and, if​necessary, fill in (x) = .​(Simplify your​answer.) B. The function is not​one-to-one. ​(b) Choose the correct graph of f and f A. −1 below. B. 10 f y −1 -10 C. 10 y 10 x 10 -10 f D. x f −1 10 f -10 −1 x -10 -10 f The function​f(x) is not​one-to-one. y 10 -10 f −1 (​ c) Give the domain and range of f and f . Begin by finding the domain and range of f(x). Select the correct choice below​ and, if​necessary, fill in any answer boxes to complete your choice. A. The domain of f is and the range of f is . ​(Type your answers in interval​notation.) B. The function is not​one-to-one. Give the domain and the range of f complete your choice. −1 . Select the correct choice below​and, if​necessary, fill in any answer boxes to A. The domain of f − 1 is and the range of f −1 is . ​(Type your answers in interval​notation.) B. The function is not​one-to-one. https://xlitemprod.pearsoncmg.com/api/v1/print/highered 15/39 5/2/22, 1:32 PM Review for Math 1314 Final Exam 50. Determine whether the function is​one-to-one. If​so, ​(a) write an equation for the inverse function in the form y = f − 1 (x)​, ​(b) graph f and f say so. −1 on the same​axes, and ​(c) give the domain and the range of f and f −1 . If the function is not​one-to-one, 3 ​f(x) = x − 9 (​ a) Write an equation for the inverse function in the form y = f any answer boxes to complete your choice. A. The function​f(x) is​one-to-one and f −1 −1 (x). Select the correct choice below​and, if​necessary, fill in ​(x) = . ​(Simplify your​answer.) B. The function is not​one-to-one. ​(b) Choose the correct graph of f and f A. −1 . The graph of f is a​blue, solid curve and f B. 10 -10 C. 10 10 -10 10 D. -10 -10 is a​red, dashed curve. The function​f(x) is not​one-to-one. 10 -10 −1 10 -10 −1 (​ c) Give the domain and range of f and f . Begin by finding the domain and range of f(x). Select the correct choice below​ and, if​necessary, fill in any answer boxes to complete your choice. A. The domain of f is and the range of f is . ​(Type your answers in interval​notation.) B. The function is not​one-to-one. Give the domain and the range of f complete your choice. −1 . Select the correct choice below​and, if​necessary, fill in any answer boxes to A. The domain of f − 1 is and the range of f −1 is . ​(Type your answers in interval​notation.) B. The function​f(x) is not​one-to-one. https://xlitemprod.pearsoncmg.com/api/v1/print/highered 16/39 5/2/22, 1:32 PM Review for Math 1314 Final Exam 51. Determine whether the function graphed is​one-to-one. 10 y Is the function graphed​one-to-one? A. Y ​ es, because each​x-value corresponds to only one​y-value, and each​y-value corresponds to only one​x-value. B. N ​ o, there is a horizontal line that intersects the graph at more than one point. x 0 -10 C. Y ​ es, every horizontal line intersects the graph at exactly one point. 10 -10 D. N ​ o, because each​x-value corresponds to every​y-value, and each​y-value corresponds to every​x-value. 52. The graph of a function f is given. Use the​horizontal-line test to determine whether f is​one-to-one. 6 y 3 x -6 -3 3 6 -3 -6 Is f​one-to-one? No Yes 53. If f​(x) = 2x ​, find f​(2.34​). f​(2.34​) ≈ ​(Round to the nearest thousandth as​needed.) 54. If f​(x) = 2x ​, find f​( − 4​). f​( − 4) = ​(Simplify your answer. Type an integer or a​fraction.) 55. Solve the equation analytically. 32x − 1 = 81 The solution set is ​(Simplify your​answer.) . 56. Solve the equation. 27 2x =9 x+1 The solution set is ​{ ​}. ​(Simplify your answer. Type an integer or a​fraction.) https://xlitemprod.pearsoncmg.com/api/v1/print/highered 17/39 5/2/22, 1:32 PM Review for Math 1314 Final Exam 57. Find the future value and interest earned if ​$8806.54 is invested for 8 years at 4​% compounded ​(a) semiannually and ​(b) continuously. (​ a) The future value when interest is compounded semiannually is approximately ​$ ​(Type an integer or decimal rounded to the nearest hundredth as​needed.) . The interest earned is approximately ​$ . ​(Type an integer or decimal rounded to the nearest hundredth as​needed.) (​ b) The future value when interest is compounded continuously is approximately ​$ ​(Type an integer or decimal rounded to the nearest hundredth as​needed.) The interest earned is approximately ​$ . . ​(Type an integer or decimal rounded to the nearest hundredth as​needed.) 58. Graph the function f(x) = − 5x + 2 . Give the domain and range. 10 y 8 Use the graphing tool to graph the function. 6 x+2 The domain of the function f(x) = − 5 is ​(Type your answer in interval​notation.) x+2 The range of the function f(x) = − 5 is ​(Type your answer in interval​notation.) 4 . 2 x . -10 -8 -6 -4 -2 2 4 6 8 10 -2 -4 -6 -8 -10 59. Graph the function ​f(x) = 3x + 1 − 2. Give the domain and range. 10 y 8 Use the graphing tool to graph the function. 6 x+1 4 The domain of the function ​f(x) = 3 − 2 is . ​(Type your answer in interval​notation.) x+1 The range of the function ​f(x) = 3 − 2 is ​(Type your answer in interval​notation.) 2 x . -10 -8 -6 -4 -2 2 4 6 8 10 -2 -4 -6 -8 -10 https://xlitemprod.pearsoncmg.com/api/v1/print/highered 18/39 5/2/22, 1:32 PM Review for Math 1314 Final Exam 60. Convert to an exponential equation. Complete the equivalent exponential equation. log 5 125 = 3 = 125 ​(Type your answer using exponential notation. Do not​ simplify.) 61. Write in logarithmic form. What is the equivalent logarithmic​form? 3 log 3 3 = 27 = ​(Simplify your answers. Type integers or​fractions.) 62. Solve. log 4 (6x − 4) = 2 Select the correct choice below and, if​necessary, fill in the answer box to complete your choice. A. The solution set is ​(Type an integer or a​fraction.) . B. The solution is the empty set. 63. Evaluate the logarithmic expression without using a calculator. Remember that log a x is the exponent to which a must be raised in order to obtain x. ​(a) log 2 16 ​(d) log 2 2 ​(b) log 3 1 ​(e) log e 1 e ​(c) log 10 0.1 2 ​(f) log 1 / 2 8 ​(a) log 2 16 = ​(Simplify your answer. Type an integer or a simplified​fraction.) ​(b) log 3 1 = ​(Simplify your answer. Type an integer or a simplified​fraction.) ​(c) log 10 0.1 = ​(Simplify your answer. Type an integer or a simplified​fraction.) ​(d) log 2 2 = ​(Simplify your answer. Type an integer or a simplified​fraction.) ​(e) log e 1 e 2 = ​(Simplify your answer. Type an integer or a simplified​fraction.) ​(f) log 1 / 2 8 = ​(Simplify your answer. Type an integer or a simplified​fraction.) https://xlitemprod.pearsoncmg.com/api/v1/print/highered 19/39 5/2/22, 1:32 PM Review for Math 1314 Final Exam 64. Use the graph of f(x) = log 3 x to graph the function f(x) = log 3 x + 1. Then give the domain and range. 20 y 16 Use the graphing tool to graph the function. 12 8 The domain is . ​(Type your answer in interval​notation.) The range is . ​(Type your answer in interval​notation.) 4 x -20 -16 -12 -8 -4 4 8 12 16 20 -4 -8 -12 -16 -20 65. Use the graph of f(x) = log 4 x to graph the function 10 ​f(x) = log 4 (x + 3). y 8 Use the graphing tool to graph the function. 6 4 2 x -10 -8 -6 -4 -2 2 4 6 8 10 -2 -4 -6 -8 -10 66. Use the properties of logarithms to rewrite the following expression as a single logarithm. Assume all variables represent positive real numbers. 6 log 2 x − 5 log 2 y 6 log 2 x − 5 log 2 y ​= https://xlitemprod.pearsoncmg.com/api/v1/print/highered 20/39 5/2/22, 1:32 PM Review for Math 1314 Final Exam 67. Write the expression as a single logarithm with coefficient 1. Assume all variables represent positive real numbers. log b x + log b y − log b u Choose the correct answer. xy A. log b u B. log b xu y C. log b xyu u D. log b xy 68. Expand. Simplify if possible. Assume that all variables represent positive real numbers. log 4 xy zt What is the expanded​expression? 69. Evaluate the following expression. Do not use a calculator. ln ln e 1 4 e = 1 4 ​(Type an integer or a​fraction.) 70. Use the​change-of-base theorem to find the logarithm. log 3 7 log 3 7 = ​(Simplify your answer. Do not round until the final answer. Then round to four decimal places as​needed.) 71. Find an approximate irrational solution to 2x = 7. Select the correct choice below and, if​necessary, fill in the answer box to complete your choice. A. The solution set is ​{ ​}. ​(Round to four decimal​places.) B. The solution is the empty set. https://xlitemprod.pearsoncmg.com/api/v1/print/highered 21/39 5/2/22, 1:32 PM Review for Math 1314 Final Exam 72. Solve the exponential equation. Express irrational solutions as decimals correct to the nearest thousandth. e x2 = 72 Select the correct choice below and, if​necessary, fill in the answer box to complete your choice. A. The solution set is . ​(Round to the nearest thousandth as needed. Use a comma to separate answers as​needed.) B. The solution is the empty set. 73. Solve for x. log 6 x + log 6 (x − 5) = 2 Select the correct choice below​and, if​necessary, fill in the answer box to complete your choice. A. The solution set is . ​(Simplify your answer. Type an integer or a decimal. Use a comma to separate answers as​needed.) B. The solution is the empty set. 74. Solve the following logarithmic equation. Use a calculator if appropriate. log (5x + 1) + log 5 = log (24x + 25) Select the correct choice below and, if​necessary, fill in the answer box to complete your choice. A. The solution set is . ​(Simplify your answer. Use a comma to separate answers as​needed.) B. The solution is the empty​set, ∅. 75. Solve the equation. ln​(3x + 5​) − lnx = ln4 Select the correct choice below and, if​necessary, fill in the answer box to complete your choice. A. The solution set is . ​(Simplify your answer. Use a comma to separate answers as​needed.) B. The solution is the empty set. https://xlitemprod.pearsoncmg.com/api/v1/print/highered 22/39 5/2/22, 1:32 PM Review for Math 1314 Final Exam 76. A population is increasing according to the exponential function y = 4 e 0.03x ​, where y is in millions and x is the number of years. How long will it take for the population to double​? Which of the following is the correct procedure to answer the​ question? A. Evaluate y = 4 e C. Evaluate y = 4 e 0.03(1 / 2) 0.03(2) . . B. Solve 4 e 0.03x = 8. D. Solve 4 e 0.03x = 2. Choose the correct answer below. A. Evaluate y = 4 e B. Solve 4 e 0.03x 0.03x . = 8. C. Evaluate y = 4 e D. Solve 4 e 0.03(1 / 2) 0.03(2) . = 2. 77. A population is increasing according to the exponential function y = 4 e 0.02x ​, where y is in millions and x is the number of years. How large will the population be in 2 ​yr? Which of the following is the correct procedure to answer the​question? A. Evaluate y = 4 e C. Evaluate y = 4 e 0.02(1 / 2) 0.02(2) . . B. Solve 4 e 0.02x = 8. D. Solve 4 e 0.02x = 2. Choose the correct answer below. A. Evaluate y = 4 e 0.02(1 / 2) . B. Solve 4 e 0.02x = 8. C. Evaluate y = 4 e 0.02(2) . D. Solve 4 e 0.02x = 2. 78. How long will it take for an investment to triple, if interest is compounded continuously at 7​%? It will take years before the investment triples. ​(Round to the nearest tenth of a​year.) 0.0359x 79. O ​ ut-of-pocket spending in a country for health care increased between 2002 and 2006. The function f(x) = 2577 e models average annual expenditures per​household, in dollars. In this​model, x represents the​year, where x = 0 corresponds to 2002. ​(a) Estimate​out-of-pocket household spending on health care in 2006. ​(b) Determine the year when spending reached ​$2833 per household. (​ a) The total expenditures per household in the year 2006 were approximately $ ​(Round to the nearest dollar as​needed.) . (​ b) During the year ​, spending reached ​$2833 per household. ​(Round down to the nearest​year.) https://xlitemprod.pearsoncmg.com/api/v1/print/highered 23/39 5/2/22, 1:32 PM Review for Math 1314 Final Exam 80. Plutonium-241 decays according to the exponential function y = y 0 e − 0.053t ​, where t is time in years. Match the given question with the correct procedure to answer the question. What is the​half-life of Plutonium-241? Choose the correct answer below. A. Evaluate y = 700 e B. Solve 1 y = y0 2 0 e − 0.053t C. Evaluate y = 700 e D. Solve 0.75y0 = y0 − 0.053(18) . − 0.053(36) e . − 0.053t . . 81. During an​epidemic, the number of people who have never had the disease and who are not immune​(they are​ susceptible) decreases exponentially according to the following ​function, where t is time in days. f(t) = 14,000 e − 0.04t Find the number of susceptible people at each time. ​(a) at the beginning of the epidemic ​(b) after 6 days ​(c) after 3 weeks (​ a) The number of susceptible people at the beginning of the epidemic is ​(Round to the nearest whole number as​needed.) (​ b) The number of susceptible people after 6 days is ​(Round to the nearest whole number as​needed.) (​ c) The number of susceptible people after 3 weeks is ​(Round to the nearest whole number as​needed.) . . . 82. Use the elimination method to solve the system of equations. 6x − 3y = 9 5x + 4y = 1 The solution set is . ​(Simplify your answer. Type an ordered​pair.) 83. Solve the system by substitution. 6x + 5y = − 4 − 5x + y = 24 The solution set is . ​(Simplify your answer. Type an ordered​pair.) https://xlitemprod.pearsoncmg.com/api/v1/print/highered 24/39 5/2/22, 1:32 PM Review for Math 1314 Final Exam 84. Solve the system. State whether the system is inconsistent or has infinitely many solutions. If the system has infinitely many​solutions, write the solution set with y arbitrary. 4x − 5y = 1 − 8x + 10y = − 2 Select the correct choice below and, if​necessary, fill in the answer box to complete your choice. A. There is one solution. The solution set is ​(Simplify your answer. Type an ordered​pair.) . B. The system has infinitely many solutions. The solution set is . ​(Simplify your answer. Type an ordered pair. Type an expression using y as the​variable.) C. The solution is the empty set. 85. Write an augmented matrix for the following system of equations and give its size. − 2x + 4y = 5 8x − 5y = 8 What is the augmented​matrix? What is the size of the​matrix? A. 2 × 3 B. 3 × 2 C. 2 × 2 D. 3 × 3 D. 4 × 3 86. Write an augmented matrix for the system of​equations, and give its size. 7x − 8y + 9z + 4 = 0 6x − 4y + 8z − 4 = 0 2y − 4z + 3 = 0 What is the augmented​matrix? What is the size of the​matrix? A. 4 × 4 B. 3 × 3 https://xlitemprod.pearsoncmg.com/api/v1/print/highered C. 3 × 4 25/39 5/2/22, 1:32 PM Review for Math 1314 Final Exam 87. Write the system of equations associated with the augmented matrix. Do not solve. 1 0 0 2 0 1 0 3 0 0 1 5 Complete the system shown below. Use the letters​x, y, and z to represent the terms from the​first, second, and third columns of the​matrix, respectively. =2 =3 =5 ​(Simplify your​answer.) 88. Write the system of equations associated with the given augmented matrix. Do not solve. 1 0 1 2 0 1 2 -4 1 0 -1 7 Choose the correct answer below. A. x+y=2 x + 2y + z = 7 x−z= −4 B. x+y=2 2y + z = − 4 x−z=7 C. x+y= −4 2y + z = 2 x−z=7 D. x+y+z=2 x + 2y + z = − 4 x+y−z=7 89. Use the​Gauss-Jordan method to solve the system of equations. If the system has infinitely many​solutions, give the solution with z arbitrary. x + y − 2z = − 22 2x − y + 8z = 106 x − 2y + 2z = 0 Select the correct choice below and, if​necessary, fill in the answer box to complete your choice. A. There is one solution. The solution set is , , ​(Simplify your​answers.) . B. There are infinitely many solutions. The solution set is where z is any real number. ​(Simplify your answers. Type expressions using z as the​variable.) , ,z ​, C. The system is inconsistent. The solution set is ∅. https://xlitemprod.pearsoncmg.com/api/v1/print/highered 26/39 5/2/22, 1:32 PM Review for Math 1314 Final Exam 90. Use the​Gauss-Jordan method to solve the system of equations. If the system has infinitely many​solutions, give the solution with z arbitrary. 2x − y + 5z = − 26 x + 2y − 3z = 27 10y + 2z = 40 Select the correct choice below and fill in any answer boxes within your choice. A. There is one solution. The solution set is , , ​(Simplify your​answers.) . B. There are infinitely many solutions. The solution set is , ,z ​, where z is any real number. ​(Simplify your your answers. Type expressions using z as the​variable.) C. The system is inconsistent. The solution set is ∅. https://xlitemprod.pearsoncmg.com/api/v1/print/highered 27/39 5/2/22, 1:32 PM Review for Math 1314 Final Exam 1. − 4 2. 104 + 52 i 3. − 1 5 4. 74 65 + 20 32 + 5. 5 + 3 i 65 i 11 ,5 − 11 6. − 4 + 4 i , − 4 − 4 i 7. − 4 5 8. 7 + ,8 53 ,7 − 53 9. 22,16 10. 3,4,5 11. A. The solution set is − 20 . (Type an integer or a simplified fraction. Use a comma to separate answers as​needed.) 12. A. The solution set is 3 . (Type an integer or a simplified fraction. Use a comma to separate answers as​needed.) 13. A. The solution set is 14. 9 . ​(Use a comma to separate answers as​needed.) 3 11 − 1, − 3, , − 2 2 15. ( − ∞,16] 16. ( − 4,1] https://xlitemprod.pearsoncmg.com/api/v1/print/highered 28/39 5/2/22, 1:32 PM 17. A. The solution set is Review for Math 1314 Final Exam − 3 7 , 4 4 . (Simplify your answer. Type an integer or a fraction. Use a comma to separate answers as​needed.) 18. 34 31 37 , 2 2 19. (x + 1)2 + y2 = 4 10 y x -10 10 -10 20. No [0,∞) ( − ∞, ∞) 21. A. The function is increasing over the open​interval(s) ( − 4,3) . (Type your answer in interval notation. Use a comma to separate answers as​needed.) A. The function is decreasing over the open​interval(s) ( − ∞, − 4) . (Type your answer in interval notation. Use a comma to separate answers as​needed.) A. The function is constant over the open​interval(s) (3,∞) . (Type your answer in interval notation. Use a comma to separate answers as​needed.) 22. 3 https://xlitemprod.pearsoncmg.com/api/v1/print/highered 29/39 5/2/22, 1:32 PM Review for Math 1314 Final Exam 23. Yes ( − ∞,3)∪(3,∞) ( − ∞,0)∪(0,∞) 24. − 4 (0,8) (2,0) − 4x + 8 25. y= 3 5 x+ 39 5 26. 6 y x -4 ( − ∞, ∞ 4 -2 G. ) 27. 4 y x -4 4 -4 F. (0, ∞ ) 28. 10 y x -10 10 -10 G. ( − ∞, ∞ ) https://xlitemprod.pearsoncmg.com/api/v1/print/highered 30/39 5/2/22, 1:32 PM Review for Math 1314 Final Exam 29. 5 y x -5 5 -5 A. No 30. 12 y x -12 D. 12 -12 [ − 1,∞) [0,∞) 31. 9 3 4 6 24 32. (1) B (2) A (3) E (4) D (5) C 33. (1) x-axis. 34. (1) y-axis. 35. − 4 36. 25 https://xlitemprod.pearsoncmg.com/api/v1/print/highered 31/39 5/2/22, 1:32 PM Review for Math 1314 Final Exam 37. − 42x − 45 ( − ∞, ∞) − 42x + 72 ( − ∞, ∞) 38. 33 39. − 70 40. ( − ∞,∞) ( − ∞,3] ( − 8,3) −8 (0, − 189) ( − 9,0),( − 7,0) 41. 2 − 8x − 9x − 27 + − 49 x−2 42. x2 − 5x + 10 − 30 43. 50 y 40 30 20 10 x -10 -8 -6 -4 -2 -10 2 4 6 8 10 -20 -30 -40 -50 https://xlitemprod.pearsoncmg.com/api/v1/print/highered 32/39 5/2/22, 1:32 PM Review for Math 1314 Final Exam 44. 100 y x -6 6 -100 B. 45. 40 y 32 24 16 8 x -10 -8 -6 -4 -2 2 4 6 8 10 -8 -16 -24 -32 -40 46. x = 2 y=3 47. x = − 3 y= −6 48. A. The inverse function is ​{ (6, − 2),(1,2),(9,5) ​}.​(Type ordered pairs. Use a comma to separate answers as​needed.) 49. A. The function​f(x) is​one-to-one and f 10 (x) = x+8 .​(Simplify your​answer.) 3 y f−1 -10 C. −1 x 10 -10 f A. The domain of f is A. The domain of f −1 ( − ∞,∞) is and the range of f is ( − ∞,∞) and the range of f ( − ∞,∞) −1 is .​(Type your answers in interval​notation.) ( − ∞,∞) . (Type your answers in interval​notation.) https://xlitemprod.pearsoncmg.com/api/v1/print/highered 33/39 5/2/22, 1:32 PM Review for Math 1314 Final Exam 50. A. The function​f(x) is​one-to-one and f −1 ​(x) = 3 x+9 . ​(Simplify your​answer.) 10 -10 A. 10 -10 A. The domain of f is A. The domain of f −1 ( − ∞,∞) is and the range of f is ( − ∞,∞) and the range of f ( − ∞,∞) −1 is .​(Type your answers in interval​notation.) ( − ∞,∞) . (Type your answers in interval​notation.) 51. B. ​No, there is a horizontal line that intersects the graph at more than one point. 52. Yes 53. 5.063 54. 1 16 55. 5 2 56. 1 2 57. 12,089.49 3282.95 12,127.73 3321.19 https://xlitemprod.pearsoncmg.com/api/v1/print/highered 34/39 5/2/22, 1:32 PM Review for Math 1314 Final Exam 58. 10 y 8 6 4 2 x -10 -8 -6 -4 -2 2 4 6 8 10 -2 -4 -6 -8 -10 ( − ∞, ∞) ( − ∞,0) 59. 10 y 8 6 4 2 x -10 -8 -6 -4 -2 2 4 6 8 10 -2 -4 -6 -8 -10 ( − ∞, ∞) ( − 2,∞) 60. 53 61. 27 3 https://xlitemprod.pearsoncmg.com/api/v1/print/highered 35/39 5/2/22, 1:32 PM Review for Math 1314 Final Exam 10 62. A. The solution set is .​(Type an integer or a​fraction.) 3 63. 4 0 −1 1 2 −2 −3 64. 20 y 16 12 8 4 x -20 -16 -12 -8 -4 4 8 12 16 20 -4 -8 -12 -16 -20 (0,∞) ( − ∞, ∞) https://xlitemprod.pearsoncmg.com/api/v1/print/highered 36/39 5/2/22, 1:32 PM Review for Math 1314 Final Exam 65. 10 y 8 6 4 2 x -10 -8 -6 -4 -2 2 4 6 8 10 -2 -4 -6 -8 -10 66. 67. 6 x log 2 5 y A. log b xy u 68. log 4 x + log 4 y − log 4 z − log 4 t 69. 1 4 70. 1.7712 71. A. The solution set is ​{ 2.8074 ​}. ​(Round to four decimal​places.) 72. A. The solution set is 2.068, − 2.068 . (Round to the nearest thousandth as needed. Use a comma to separate answers as​needed.) 73. A. The solution set is 9 . (Simplify your answer. Type an integer or a decimal. Use a comma to separate answers as​needed.) 74. A. The solution set is 20 .​(Simplify your answer. Use a comma to separate answers as​needed.) https://xlitemprod.pearsoncmg.com/api/v1/print/highered 37/39 5/2/22, 1:32 PM Review for Math 1314 Final Exam 75. A. The solution set is 5 .​(Simplify your answer. Use a comma to separate answers as​needed.) 76. B. Solve 4 e 0.03x = 8. 77. C. Evaluate y = 4 e 0.02(2) . 78. 15.7 79. 2975 2004 80. B. Solve 1 y = y0 2 0 e − 0.053t . 81. 14,000 11,013 6044 82. (1, − 1) 83. ( − 4,4) 84. B. The system has infinitely many solutions. The solution set is 1 + 5y 4 ,y . (Simplify your answer. Type an ordered pair. Type an expression using y as the​variable.) 85. − 2 4 5 8 −5 8 A. 2 × 3 https://xlitemprod.pearsoncmg.com/api/v1/print/highered 38/39 5/2/22, 1:32 PM Review for Math 1314 Final Exam 86. 7 −8 9 −4 6 −4 8 4 0 2 −4 −3 C. 3 × 4 87. x y z 88. x+y =2 2y + z = − 4 B. x − z = 7 89. A. There is one solution. The solution set is −4 , 14 , 16 . 2 , 5 , −5 . (Simplify your​answers.) 90. A. There is one solution. The solution set is (Simplify your​answers.) https://xlitemprod.pearsoncmg.com/api/v1/print/highered 39/39