Section 3.6 Functions 273 Applications Without functions, many things in life would be very chaotic. Functions enable our mail to be delivered properly since each address can only correspond to one location. Functions enable our login to different programs to work properly since each login name must correspond to exactly one person. Every social security number must correspond to exactly one person. The list of these types of situations is infinite. In Example 6, we will see a function that relates to a real-world situation. �� ������������������������ ������������������ According to the U.S. Department of Labor, the fastest-growing occupation for the years 2006–2016 is a network system and data communications analyst. The function f (x) = 1343x��+ 45,657 approximates the median salary in the United States for x years of experience in this field. (Sources: www.bls.gov and www .payscale.com) 6a. Find the median salary with 5 yr of experience. 6b. How many years of experience is required for the median salary to be $60,430? Solutions 6a. The input x represents the number of years of experience and f (x), or y, represents the median salary. To find the salary with 5 yr of experience, we let x = 5. f (x) = 1343x + 45,657 f (5) = 1343(5) + 45,657 = 6715 + 45,657 = 52,372 The median salary is $52,372 with 5 yr of experience. 6b. To find how many years of experience is required for the salary to be $60,430, we set f (x) = 60,430 and solve for x. 1343x + 45,657 = 60,430 1343x + 45,657 - 45,657 = 60,430 - 45,657 Subtract 45,657 from each side. 1343x = 14,773 Divide each side by 1343. x = 11 Simplify. The median salary is $60,430 with 11 yr of experience. Student Check 6 The number of cell-phone subscribers in the United States, in millions, between 1985 and 2009 can be approximated by f (x) = 0.7082x2 - 4.0318x + 4.8661, where x is the number of years after 1985. Use the function to determine the number of cell phone subscribers in the United States in 2015. (Source: www.infoplease.com) Troubleshooting Common Errors Some common errors associated with the concept of functions are shown next. �� ������������������������ ������������������ A problem and an incorrect solution are given. Provide the correct solution and an explanation of the error. 7a. Is the relation {(-2, 3), (-1, 0), (0, -1), (1, 0), (2, 3)} a function? �������������������������������������� ���������������������������������������������������������������� The relation is a function. The definition of a function is that each x-value have only one output. It is OK if the output values repeat. Since every value of x has only one output, this relation is a function. Objective 6 ▶ Apply functions to real-life applications. Objective 7 ▶ Troubleshoot common errors. The relation o is s not ot a a function since two o x-va values ues co correspond to the same y-value. Both -2 and 2 have a y-value of 3.
hendricks_beginning_algebra_1e_ch1_3
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