Chapter 4 Introduction to Relations and
Functions For Exercises 1124, find the domain
and range of the relations. Use interval notation
where appropriate. 11. 12. 13. 14. 15. 16. 17.
18. 19. 20. y x 5
be defined by several different methods: by a
list of ordered pairs, by a correspondence
between the domain and range, by a graph, or
by an equation. Skill Practice Example 2 The xand y-components tha
function is defined as a relation with the added
restriction that each value in the domain must
have only one corresponding y-value in the
range. In mathematics, functions are often
given by rules or
can be found using a Table feature. Function
values can also be evaluated by using a Value
(or Eval) feature. The value of g142 is shown
here. Y1 1 2x 1 g1x2 Calculator Connections
Skill Practice Answ
Skills 29. a. Define a relation with four ordered
pairs such that the first element of the ordered
pair is the name of a friend and the second
element is your friends place of birth. b. State
the doma
Set of second coordinates 1. Find the domain
and range of the relation. e 10, 02, 18, 42, a 1
2 , 1b, 13, 42, 18, 02 f Skill Practice Example 1
Table 4-1 Definition of a Relation in x and y Any
set of
Relation 2. Applications Involving Relations
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Page 256 IA CONFIRMING PAGES Section 4.1
Introduction to Relations 257 Finding the
Domain and Range of a Relation Fi
Definition of a Quadratic Function 4. Finding the
x- and yIntercepts of a Function Defined by y = f
(x ) 5. Determining Intervals of Increasing,
Decreasing, or Constant Behavior Definition of a
Linear
2. The shape of the graph of a quadratic
function. 3. A function whose graph is a
horizontal line. 6. A function whose graph is a
line that is not vertical or horizontal. 7. The set
of second coordina
the function at . Use these values to support
your answer to Exercise 80. 99. a. Graph on a
viewing window defined by and b. Use the
graph to approximate the function at . Use
these values to support
the function, produce a real number. The range
of f is the set of all y-values corresponding to
the values of x in the domain. To find the
domain of a function defined by keep these
guidelines in mind
more than once y x Not a Function A vertical
line intersects in more than one point. 5 1 4 3 3
4 5 2 1 3 4 5 1 2 1 4 5 2 3 Function No vertical
line intersects more than once. y x 5 1 4 3 3 4 5
2 1 3
Introduction to Relations and Functions 4.1
Introduction to Relations 4.2 Introduction to
Functions 4.3 Graphs of Functions 4.4 Variation
255 In this chapter we introduce the concept of
a function. In
Section 4.1 Introduction to Relations 263 21.
22. 23. 24. Concept 2: Applications Involving
Relations 25. The table gives a relation between
the month of the year and the average
precipitation for tha
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PAGES Section 4.1 Introduction to Relations 261
Study Skills Exercises 1. Compute your grade at
this point. Are you earning the grade that you
want? If not, ma
U.S. National Oceanic and Atmospheric
Administration Age Maximum Recommended
Heart (years) Rate (Beats per Minute) y x 20 200
30 190 40 180 50 170 60 160
miL2872X_ch04_255-308 9/25/06 11:51 AM
Page 26
as a set of ordered pairs. 3. 4. 5. 6. 7. List the
domain and range of Exercise 3. 8. List the
domain and range of Exercise 4. 9. List the
domain and range of Exercise 5. 10. List the
domain and range
height. Based on these data, a forensics
specialist or archeologist can find a linear
relationship between height y and femur length
x: From this type of relationship, the height of a
woman can be inf
and constant functions, the following equations
define six basic functions that will be
encountered in the study of algebra: Equation
Function Notation The graph of the function
defined by is linear,
Find the domain and range of the relations:
Solution: a. Domain: cfw_3, 2, 7 Range: cfw_9
Example 3 Figure 4-3 y x 5 4 3 2 1 1 2 3 4 5 5 4 3
2 1 1 2345 x y2 2 3 7 9 x y Figure 4-1 3 1 3 4 2 x
y Domain
domain because any real number substituted
for t will produce a real number. The domain is
the set of all real numbers. Interval notation:
Write the domain of the functions in interval
notation. 12. 1
element in the domain? d. Complete the
ordered pair: (50, ) e. Complete the ordered
pair: ( , 190) 27. The population of Canada, y, (in
millions) can be approximated by the relation
where x represents
not f x. miL2872X_ch04_255-308 9/25/06 11:52
AM Page 268 CONFIRMING PAGES d. We say g
of is . This is equivalent to the ordered pair
Notice that and correspond to the ordered pairs
and In the graph, t
and the range elements are the y-coordinates.
Domain: cfw_2, 1, 0, 1, 2 Range: cfw_3, 0, 1 c. The
domain consists of an infinite number of xvalues extending from 8 to 8 (shown in red).
The range consi
and 8 x 86 or 38, 84 5x x is a real number
and y x Skill Practice Answers 3. Domain cfw_5, 2,
4, range cfw_0, 8, 15, 16 4. Domain cfw_4, 0, 1, 4,
range cfw_5, 3, 1, 2, 4 5. Domain: or [4, 0], range:
o