204 Chapter 2 Linear Equations in Two Variables and Functions 98. Brian’s score on an exam is a function of the number of hours he spends studying.The function defined by 100x2 50 x2 P1x2 (x 0) indicates that he will achieve a score of P% if he studies for x hours. Evaluate P(0), P(5), P(10), P(15), P(20), and P(25) and confirm the values on the graph. (Round to one decimal place.) Interpret P(25) in the context of this problem. A Student Score (Percent) as a Function of Study Time B 70 60 50 For Exercises 99–102, write a function defined by y f(x) subject to the conditions given. Expanding Your Skills For Exercises 103–104, write the domain in interval notation. 103. 104. Graphing Calculator Exercises p1x2 8 1x 4 q1x2 2 1x 2 C D E F k1t2 1t 5. 106. Graph Use the graph to support 105. Graph Use the graph to support your answer to Exercise 86. h1t2 1t 7. your answer to Exercise 85. 1. Linear and Constant Functions A function may be expressed as a mathematical equation that relates two or more variables. In this section, we will look at several elementary functions. We know from Section 2.1 that an equation in the form ,where k is a constant, is a horizontal line. In function notation, this can be written as For example, the graph of the function defined by is a horizontal line, as shown in Figure 2-35. We say that a function defined by is a constant function because for any value of x, the function value is constant. f1x2 k f1x2 3 f1x2 k. y k f (x) x 5 4 2 1 543 21 1 2 3 4 5 1 2 3 4 5 f(x) 3 3 Figure 2-35 100 0 0 5 10 15 20 25 30 Percent Study Time (hr) 90 80 40 30 20 10 x P(x) 99. The value of f(x) is three more than two times x. 101. The value of f(x) is ten less than the absolute value of x. 100. The value of f(x) is four less than the square of x. 102. The value of f(x) is sixteen times the square root of x. Section 2.7 Graphs of Functions Concepts 1. Linear and Constant Functions 2. Graphs of Basic Functions 3. Definition of a Quadratic Function 4. Finding the x- and y-Intercepts of a Graph Defined by y f (x)
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