1.2. SETS AND EQUIVALENCE RELATIONS 5
for the union and intersection, respectively, of the sets A1, . . . ,An.
When two sets have no elements in common, they are said to be
disjoint; for example, if E
4 CHAPTER 1. PRELIMINARIES
for a set containing elements 331, m2, . . . , mm or
X : cfw_11: : 3: satises P
if each as in X satises a certain property P. For example, if E is the set
of even positive i
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 lin
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
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 i
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
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
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
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 po
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.
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 re
Student Solution Manual 163
5. You can solve by substitution (isolating
x or
y ), graphically, or by addition.
7. Yes
9. Yes
11.
(~19 2)
13.
(3? 1)
15.
6% o)
17. No solutions exist.
19.
(152, 532)
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
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
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 imagina
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 tautulug
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, det
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 follow