226 Chapter 3 Functions
in this section, you will:
Determine whether a relation represents a function. E
Find the value of a function.
Determine whether a function is oneto-one.
Use the vertical line test to identify functions.
Graph the functions liste
256 Chapter 3 Functions
3.2. | etnaiti and Range
In this section, you will:
E Find the domain of a function dened by an equation.
2.2 Graph piecewise-defined functions.
If youre in the mood for a scary movie, you may want to check out one of the five
Chapter 2 Equations and lnequalities 189
in this section you will:
Solve equations involving rational exponents. 53m 3%.
Solve equations using factoring.
Solve radical equations.
Solve absolute value equations.
Solve other types of equations.
We hav
204 Chapter 2 Equations and Inequalities
2.? l Maser inequaiites and anaemia Vaiee ineqaaiities
Learning. Obiecthies
In this section you will:
2521: Use interval notation.
3.16:5 Use properties of inequalities. . i
p 22.3 Solve inequalities in one varia
Student Solution Mama 12
257.
4 + 4a3c~16ac3 6'cd
. The terms of a polynomial do no: have to have a common factor for the entire polynomial to be factorable. For example,
"93; dont have a common factor, but the whole polynomial is sti factorable:
4x
Factoring Supplement
Factoring Using Substitution
3-Terms
Step 1: If there is a greatest common factor (GCF) between all 3 terms, factor it
out. Do not forget to include the GCF as part of your final answer.
Step 2: Let w equal the polynomial in the first
Student Soiution Manual 9
107.
72a2
812:
1113 0.00135 m
115.
1.0995x1012
117. 0.000000000013397 in.
119. 12230590464
m 66
121.
a 14
l 296
123.
11
(196
125.
._1_
(106396 6
W127w 0 D00000000000000000000000000000000662606957
28 When there 15 no index, it i
Student Soiutton Mama!
5. The xintercept is
(2, 0)
(O, 6).
7. The x-intercept is
(2 O) and they-intercept is
(O, ~3).
9. The xdntercept is
(3, 0)
(o. g)
and cfw_he yintercept is
and the y-intercept is
m
w W H 3
x,
he
9.
W
F
w
W
W
M
, 4333 M
Wm. wwwm ww
Student Solution Manual
53.
440 - 10) + 5
55. irrational number
57.
g + 400 - 2(600) 2 1200
59. inverse praperty of addition
61. 68.4
63. true
65. irraxional
67. rational
69. No, the two expressions are not the same. An exponent. tells haw many times yo
Student Solution Manual 25
41,
43.
d = 8.246
45.
d :2 5
47.
(3, 4)
49.
x = 0 y = 2
51.
x = 0.75 y = 0
53.
x: 1.667 =0
55.
15"? 3 3-8 mi sherter
57.
6.042
59. Midpoint of each diaganal is the same point
(2 2) Note this is a characteristic of rectamgles
Student Sotumn Manuai
2. 0 . . . .
( , ) IS a zero With muitiphmty 2, and the graph bounces off cfw_he xaxis at this point,
(2., 0)
, IS a single zero and the graph crosses the axis at this point.
Mmmmmmwmmmmmmramwyw
5:46
51 : 39
Section
Student Solution Manual 7
1.57.
(x + 5)(x + 6)
(x + 2)(x + 4
1.58
1
1.59.
2(x-7)
(x + 5)(x3)
1.60.
Section Exercises
1. National number. The square root of two does no: terminate, and it does not repeat a pattern. It cannot be written as a quotient
of t
Student Solution Manual 28
117.
The slope for (l, l) [0 (0i 4) is 3.
The slope for (1. l) to cfw_2, 0) is :3;-
The slope for (2, O) to (3. 3) is 3.
The slope for (0, 4) [0 (3, 3) is 13,-1-
Yes they are perpendicular.
119. 30 ft
121. $57.50
123. 220 mi
3
Student Sofution Manual 119
529.
r(V) =
.
'4 1.99 inches
531. The graph will have the appearance of a power function,
533, N0. Multiple variables may jointly vary.
535.
y = 5x
537.
y = 10x3
2 Student Solution Manua! 120
573.
y = vb?
577. 1.89 years
57
Student Solution Manual 29
1?4.
r = g;
176.
.anMMK/WMQ; = 127:
178. Add the real parts together and the imaginary parts together.
180. Possible answer:
i times
i equals 1, which is not imaginary.
182.
8 + 21
184.
14 + 7:
186.
_E 1.5;
29 + 29
188.
Ex 2: Cemplete the truth table for the following eeuditieuel statement- [p . :3 cfw_p V q
This kind enfsteteuleut= where it is true for ever? ease efp eudq being true er false= is
ealled a tautulugy- Ex 2: Complete the truth table for the following con
E; l: Censtruet a truth table fer the eempeuuel statement M-
New: determine the truth value efgggj if p is true and q is false. Ex 1: Construct a truth table for the compound statement M.
New, determine the truth value ufng if p is true and q is false
1. Graph f(x) =
x . Plot at least three points.
a. Use f(x) graph to graph g(x) =
x 1.
b. Use f(x) graph to graph j(x) = x1
2. Let f(x) = x . Use the graph of f(x) from Example 1 to graph the following
functions, also state their domains and ranges.
a.
1. Determine analytically if the following functions are even, odd or neither.
3
2
a. f(x) = x + x + x + 1
b. f(x) =
1x 2
2. Use the graph of y = f(x) given below to answer the questions.
f(x)
6
4
2
-5
-4
-3
-2
-1
0
-2
-4
-6
a. Find the domain of f.
b. F
1. Determine analytically if the following functions are even, odd or neither.
3
2
a. f(x) = x + x + x + 1
b. f(x) =
1x 2
2. Use the graph of y = f(x) given below to answer the questions.
f(x)
6
4
2
-5
-4
-3
-2
-1
0
-2
-4
-6
a. Find the domain of f.
b. F