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EXAMPLE 9 Graph f (x) y-intercept. Solution f (x) c c m x y 5 f(x) x 1 13 5 5 (0, 1) 5 (3, 2) To graph this function, fi rst plot the y-intercept, (0, 1), then use the slope to locate another point on the line. YOU TRY 9 Graph f (x) 1 3 x 1 using the slope and 1 3 x 1 1 3 y-int: (0, 1) 3 4 x 2 using the slope and y-intercept. 7 Solve Problems Using Linear Functions The independent variable of a function does not have to be x. When using functions to model real-life problems, we often choose a more “meaningful” letter to represent a quantity. For example, if the independent variable represents time, we may use the letter t instead of x. The same is true for naming the function. No matter what letter is chosen for the independent variable, the horizontal axis is used to represent the values of the independent variable, and the vertical axis represents the function values. EXAMPLE 10 A compact disc is read at 44.1 kHz (kilohertz). This means that a CD player scans 44,100 samples of sound per second on a CD to produce the sound that we hear. The function S(t) 44.1t tells us how many samples of sound, S(t), in thousands of samples, are read after t seconds. (www.mediatechnics.com) a) How many samples of sound are read after 20 sec? b) How many samples of sound are read after 1.5 min? c) How long would it take the CD player to scan 1,764,000 samples of sound? d) What is the smallest value t could equal in the context of this problem? e) Graph the function. Solution a) To determine how much sound is read after 20 sec, let t 20 and fi nd S(20). S(t) 44.1t S(20) 44.1(20) Substitute 20 for t. S(20) 882 Multiply. S(t) is in thousands, so the number of samples read is 882 1000 882,000 samples of sound. www.mhhe.com/messersmith SECTION 4.5 Introduction to Functions 207


messersmith_power_intermediate_algebra_1e_ch4_7_10
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