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Most graphing calculators have an option under the zoom menu that does this automatically. qxd 11/22/2007 06:15 PM Page 27 pinnacle 110:MHIA064:mhbar3:SE:CH 01: S E C T I O N 1–2 Functions 27 One way to determine if an equation defines a function is to examine its graph. The graphs of the equations y ϭ x2 Ϫ 4 and x2 ϩ y2 ϭ 16 are shown in Figure 1. y Z Figure 1 Graphs of equations and the vertical line test. * Each vertical line intersects the parabola in exactly one point. This shows that to each value of the independent variable x there corresponds exactly one value of the dependent variable y.

Letters other than f and x can be used to represent functions and independent variables. For example, g(t) ϭ t 2 Ϫ 3t ϩ 7 defines g as a function of the independent variable t. To find g(Ϫ2), we replace t by Ϫ2 wherever t occurs in g(t) ϭ t 2 Ϫ 3t ϩ 7 and evaluate the right side: g(؊2) ϭ (؊2)2 Ϫ 3(؊2) ϩ 7 ϭ4ϩ6ϩ7 ϭ 17 Thus, the function g assigns the range value 17 to the domain value Ϫ2; the ordered pair (Ϫ2, 17) belongs to g. qxd 11/22/2007 06:15 PM Page 32 pinnacle 110:MHIA064:mhbar3:SE:CH 01: 32 CHAPTER 1 FUNCTIONS, GRAPHS, AND MODELS It is important to understand and remember the definition of the symbol f (x): Z DEFINITION 4 The Symbol f(x) The symbol f(x), read “f of x,” represents the real number in the range of the function f corresponding to the domain value x.

X y 35 40 45 (B) Does the demand increase or decrease if the price is increased from $40 to $45? By how much? (C) Does the demand increase or decrease if the price is decreased from $40 to $35? By how much? 71. PRICE AND REVENUE Refer to Problem 69. The revenue from the sale of x cases of paper at $y per case is given by the product R ϭ xy. (A) Use the results from Problem 69 to complete the following table of revenues. 66. MANUFACTURING A box with a lid is to be cut out of a 10-inch by 20-inch sheet of thin cardboard by cutting out six x-inch squares and folding as indicated in the figure.

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College Algebra - Graphs and Models by R. Barnett, et. al.


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