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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 See the Internal Revenue Service’s website 7 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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