Part 2

1. Evaluate the function at each specified value of the independent variable and simplify

(a) (b) (c)

Find the difference quotient and simplify your answer

2.

3.

Use function notation to write gin terms of the common function f.

4.

5

6. .

7.

8.

Use a graphing utility to graph the function and determine whether the function is one-to-one. Explain the reason

9. 10.

11. GeometryA rectangular package to be sent by the U.S. Postal Service can have a maximum combined length and girth (perimeter of a cross section) of 108 inches.

(a)Write the volume of the package as a function of x.

(b)What is the domain of the function?

(c)What dimensions will maximize the volume of the package?

12.The suggested retail price of a new car is pdollars. The dealership advertised a factory rebate of $1200 and an 8% discount.

(a)Write a function Rin terms of p,giving the cost of the car after receiving the rebate from the factory.

(b)Write a function Sin terms of p,giving the cost of the car after receiving the dealership discount.

(c)Form the composite functions and and interpret each.

(d)Find andWhich yields the lower cost for the car? Explain

13. ProfitThe profit Pper week on a certain product is given by the model where xis the amount spent on advertising. In this model,xand Pare both measured in hundreds of dollars.

(a)Use a graphing utility to graph the profit function.

(b)The business estimates that taxes and operating costs will increase by an average of $2500 per week during the next year. Rewrite the profit equation to reflect this expected decrease in profits. Identify the type of transformation applied to the graph of the equation.

(c)Rewrite the profit equation so that xmeasures advertising expenditures in dollars. [Find Identify the type of transformation applied to the graph of the profit function

Find two functions fand gsuch that (There are many correct answers.)

14.

15.

16.

17.

Match the graph of the function with the graph of its inverse and explain the choice

(a) (b) (c)

18. 19. 20.

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Use the functions and to find the specified functions.

21. (1) 22. (-2) 23. (3) 24. (-4)