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Evaluating a Function In Exercises 5–12,
evaluate the function at the given value(s) of the
independent variable. Simplify the results.f (x) = 3x − 2
(c) f (b)
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- The figure shows the graphs of the cost and revenue functions for a company that manufactures and sells small radios. Use the information in the figure to solve Exercises 67–72. 35,000 30,000 C(x) = 10,000 + 30x 25,000 20,000 15,000 R(x) = 50x 10,000 5000 100 200 300 400 500 600 700 Radios Produced and Sold 67. How many radios must be produced and sold for the company to break even? 68. More than how many radios must be produced and sold for the company to have a profit? 69. Use the formulas shown in the voice balloons to find R(200) – C(200). Describe what this means for the company. 70. Use the formulas shown in the voice balloons to find R(300) – C(300). Describe what this means for the company. 71. a. Use the formulas shown in the voice balloons to write the company's profit function, P, from producing and selling x radios. b. Find the company's profit if 10,000 radios are produced and sold. 72. a. Use the formulas shown in the voice balloons to write the company's profit function,…In Exercises 41–48, write a piecewise formula for the function.Section 2.4: Chain Rule In Exercises 9–34, find the derivative of the function.
- In Exercises 65–68, find and sketch the domain of ƒ. Then find an equation for the level curve or surface of the function passing through the given point.Exercises 31–38: Determine if f is a linear or nonlinear function. If f is a linear function, determine if f is a constant function. Support your answer by graphing f. -2 35. f (x) = |x + 1|Even and Odd FunctionsIn Exercises 47–58, say whether the function is even, odd, or neither. Give reasons for your answer.
- The function f(x) = 0.4x2 – 36x + 1000 models the number of accidents, f(x), per 50 million miles driven as a function of a driver's age, x, in years, for drivers from ages 16 through 74, inclusive. The graph of f is shown. Use the equation for f to solve Exercises 45–48. 1000 flx) = 0.4x2 – 36x + 1000 16 45 74 Age of Driver 45. Find and interpret f(20). Identify this information as a point on the graph of f. 46. Find and interpret f(50). Identify this information as a point on the graph of f. 47. For what value of x does the graph reach its lowest point? Use the equation for f to find the minimum value of y. Describe the practical significance of this minimum value. 48. Use the graph to identify two different ages for which drivers have the same number of accidents. Use the equation for f to find the number of accidents for drivers at each of these ages. Number of Accidents (per 50 million miles)In Exercises 61–64, find an equation for the level surface of the function through the given point.In Exercises 29–30, find f(-x) – f(x) for the given function f. Then simplify the expression. 29. f(x) = x + x - 5 30. f(x) = x² – 3x + 7
- U.S. Population The U.S. population can be modeledfor the years 1960–2060 by the function p = 2.6x +177, where p is in millions of people and x is in yearsfrom 1960. During what year does the model estimatethe population to be 320,000,000?(Source: www.census.gov/statab)Use this information to solve Exercises 9–11:A company is planning to produce and sell a new line of computers. The fixed cost will be $360,000 and it will cost $850 to produce each computer. Each computer will be sold for $1150. 9. Write the cost function, C, of producing x computers. 10. Write the revenue function, R, from the sale of x computers. 11. Determine the break-even point. Describe what this means.. Marriage Rate The marriage rate per 1000 unmarriedwomen for the years 1987–2014 can be modeled bythe function 132x + 1000y = 9570, where x is thenumber of years after 1980. During what year doesthe equation indicate the marriage rate will be 4.29?(Source: National Vital Statistics Report 2010)