Concept explainers
Consumer Issues. You work in a department store in which employees are entitled to a 30% discount on their purchases. You also have a coupon worth $5 off any item. Let x represent the retail price of an item,
a. Write a function ix) that models discounting an item by 30%.
b. Write a function g(x) that models applying the coupon.
c. Use a composition of your two functions from (a) and (b) to model your cost for an item assuming that the clerk applies the discount first and then the coupon.
d. Use a composition of your two functions from (a) and (b) to model your cost for an item assuming that the clerk applies the coupon first and then the discount.
e. Use the composite functions from (c) and (d) to find how much more an item costs assuming that the clerk applies the coupon first.
Want to see the full answer?
Check out a sample textbook solutionChapter 1 Solutions
PRECALC: UNIT CIRCLE (LL) W/18WK MYLAB
- How do you find the domain for the composition of two functions, fg ?arrow_forwardWhat is the difference between the input and the output of a function?arrow_forwardUse your schools library, the Internet, or some other reference source to find real-life applications of approximations of functions.arrow_forward
- Suppose you have a job that pays $8.50 per hour and you work anywhere from 10 to 40 hours per week. a. Write an equation, with a restriction on the variable x, that gives the amount of money, y, you will earn for working x hours in one week. b. Use the function rule you have written in part (a) to complete Table 4. c. Construct a line graph from the information in Table 4. d. State the domain and range of this function.arrow_forwardHigh School Graduates The following table shows the number, in millions, graduating from high school in the United States in the given year. Year Number graduating in millions 1985 2.83 1987 2.65 1989 2.47 1991 2.29 a. By calculating difference, show that these data can be modeled using a linear function. b. What is the slope for the linear function modeling high school graduations? Explain in practical terms the meaning of the slope. c. Find a formula for a linear function that models these data. d. Express, using functional notation, the number graduating from high school in 1994, and then use your formula from part c to calculate that value.arrow_forwardWhat is the composition of two functions, fg ?arrow_forward
- Trigonometry (MindTap Course List)TrigonometryISBN:9781305652224Author:Charles P. McKeague, Mark D. TurnerPublisher:Cengage LearningGlencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw HillFunctions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageElementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage Learning