Evaluating a Function In Exercises 5–12,evaluate the function at the given value(s) of theindependent variable. Simplify the results.f (x) = 3x − 2 (c) f (b)
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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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- 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.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|
- 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.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)Even and Odd FunctionsIn Exercises 47–58, say whether the function is even, odd, or neither. Give reasons for your answer.
- 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 + 7U.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.In Exercises 1–4, (a) write a formula for the function and (b) use theformula to find the indicated value of the function.1. the area A of a circle as a function of its diameter d; the area of acircle of diameter 4 in.2. the height h of an equilateral triangle as a function of its side lengths; the height of an equilateral triangle of side length 3 m3. the surface area S of a cube as a function of the length of thecube’s edge e; the surface area of a cube of edge length 5 ft4. the volume V of a sphere as a function of the sphere’s radius r;the volume of a sphere of radius 3 cm. 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)