184 Chapter 3 Graphs, Relations, and Functions Student Check 3 Find the requested information. a. Find g(-5) if g(x) = -2x2 - 4x + 1. b. Let f (x) = 9x + 4. Find f (0) and find x such that f (x) = 0. c. Let c(x) be given by Y1. Find c(2) and find x such that c(x) = 4.5. d. Let f (x) be given by the graph. Find f (-2) and find x such that f (x) = -3. 2 2 4 –2 –4 –2 –4 –6 x y Applications We encounter functions every day of our lives. Every time we go to the grocery store and an item is scanned, a price appears on the register. This function pairs together an item with its price. Have you ever registered to use a password-protected software program? Have you ever entered a login name only to receive the message that the name you entered has already been used? This is because a login name must be assigned to only one person. This function pairs together login name to the person. There are many other examples of functions from the real world. In Example 4, we will see a function that relates to a real-world situation. Objective 4 Examples 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 models the median salary in the United States for x years of experience. (Source: http://www.bls.gov and http://www.payscale.com) 4a. Find the median salary with 5 yr of experience. 4b. How many years of experience is required for the median salary to be $60,430? Solutions 4a. 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 Replace x with 5. f (5) = 6715 + 45,657 Multiply. f (5) = 52,372 Add. So, the median salary is about $52,372 with 5 yr of experience. 4b. 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. f (x) = 1343x + 45,657 60,430 = 1343x + 45,657 Replace f(x) with 60,430. 60,430 - 45,657 = 1343x + 45,657 - 45,657 Subtract 45,657 from each side. 14,773 = 1343x Simplify. 14,773 1343 = 1343x 1343 Divide each side by 1343. 11 = x Simplify. So, the median salary is about $60,430 with 11 yr of experience. Objective 4 ▶ Apply functions to real life.
hendricks_intermediate_algebra_1e_ch1_3
To see the actual publication please follow the link above