College Algebra 9th txtbk

SECTION 2–1 Cartesian Coordinate Systems 113
Graphs illustrate the relationship between two quantities, one represented by x coordinates
and the other by y coordinates. If no equation for the graph is available, we can find
specific examples of this relationship by estimating coordinates of points on the graph.
Example 2 illustrates this process.
EXAMPLE 2
Ozone Levels
The ozone level during a 12-hour period in a suburb of Milwaukee, Wisconsin, on a particular
summer day is given in Figure 6, where L is ozone in parts per billion and t is time
in hours. Use this graph to estimate the following ozone levels to the nearest integer and
times to the nearest quarter hour.
(A) The ozone level at 6 P.M.
(B) The highest ozone level and the time when it occurs.
(C) The time(s) when the ozone level is 90 ppb.
120
L
100
Parts per billion (ppb)
80
60
40
20
0
Noon
1 2 3 4 5 6 7 8 9 10 11 12
t
Z Figure 6 Ozone level.
SOLUTIONS
(A) The L coordinate of the point on the graph with t coordinate 6 is approximately 97 ppb.
(B) The highest ozone level is approximately 109 ppb at 3 P.M.
(C) The ozone level is 90 ppb at about 12:30 P.M. and again at 10 P.M.
MATCHED PROBLEM 2
Use Figure 6 to estimate the following ozone levels to the nearest integer and times to the
nearest quarter hour.
(A) The ozone level at 7 P.M.
(B) The time(s) when the ozone level is 100 ppb.
Z Using Symmetry as an Aid in Graphing
We noticed that the graph of y x 2 4 in Example 1 is symmetric with respect to the y
axis; that is, the two parts of the graph coincide if the paper is folded along the y axis. Similarly,
we say that a graph is symmetric with respect to the x axis if the parts above and