Unformatted text preview: es,5 income tax formulas6 ) are
modeled by such functions. Also note that the domain of h in the above example is restricted to
t ≥ 0. For example, h(−3) is not deﬁned because t = −3 doesn’t satisfy any of the conditions in any
of the function’s pieces. There is no inherent arithmetic reason which prevents us from calculating,
say, −5(−3)2 + 100(−3), it’s just that in this applied setting, t = −3 is meaningless. In this case,
we say h has an applied domain7 of [0, ∞) 5 See the United States Postal Service website http://www.usps.com/prices/ﬁrst-class-mail-prices.htm
See the Internal Revenue Service’s website http://www.irs.gov/pub/irs-pdf/i1040tt.pdf
or, ‘explicit domain’
6 50 Relations and Functions 1.5.1 Exercises 1. Suppose f is a function that takes a real number x and performs the following three steps in
the order given: (1) square root; (2) subtract 13; (3) make the quantity the denominator of
a fraction with numerator 4. Find an expression for f (x) and ﬁnd its domain.
2. Suppose g is a f...
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