SECTION 10.1 Inverse Functions 577
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10.1 EXERCISES
In Exercises 1– 4, write a few sentences of explanation. See Example 1.
1.A study found that the trans fat content in fast-food products varied widely around the
world, based on the type of frying oil used, as shown in the table. If the set of countries is
the domain and the set of trans fat percentages is the range of the function consisting of
the six pairs listed, is it a one-to-one function? Why or why not?Source:New England Journal of Medicine.Percentage of Trans Fat
Country in McDonald’s Chicken
Scotland 14
France 11
United States 11
Peru 9
Russia 5
Denmark 1Source:U.S. Environmental Protection
Agency.State Number of Sites
New Jersey 116
California 97
Pennsylvania 96
New York 86
Michigan 67
Florida 52
Illinois 49
Texas 492.The table shows the number of uncontrolled haz-
ardous waste sites in 2008 that require further inves-
tigation to determine whether remedies are needed
under the Superfund program. The eight states listed
are ranked in the top ten on the EPA’s National Prior-
ity List.
If this correspondence is considered to be a
function that pairs each state with its number of
uncontrolled waste sites, is it one-to-one? If not,
explain why.3.The road mileage between Denver, Colorado,
and several selected U.S. cities is shown in the
table. If we consider this as a function that
pairs each city with a distance, is it a one-to-
one function? How could we change the an-
swer to this question by adding 1 mile to one of
the distances shown?Distance to Denver
City (in miles)
Atlanta 1398
Dallas 781
Indianapolis 1058
Kansas City, MO 600
Los Angeles 1059
San Francisco 12354.Suppose you consider the set of ordered pairs such that xrepresents a person in
your mathematics class and yrepresents that person’s father. Explain how this function
might not be a one-to-one function.In Exercises 5– 8, choose the correct response from the given list.
5.Concept Check If a function is made up of ordered pairs in such a way that the same
y-value appears in a correspondence with two different x-values, then
A.the function is one-to-one B.the function is not one-to-one
C.its graph does not pass the vertical line test
D.it has an inverse function associated with it.1 x, y 2