MATH 1111 COMPREHENSIVE FINAL EXAM REVIEW ANSWER KEY RALSTON

PART I: Identify the type function represented by each of the following algebraic representations: Absolute Value, Constant, Cube Root, Cubic, Exponential, Linear, Logarithmic, Polynomial, Quadratic, Rational, or Square Root

PART II: Identify the type function represented by each of the following graphical representations: Absolute Value, Constant, Cube Root, Cubic, Exponential, Linear, Logarithmic, Polynomial, Quadratic, Rational, or Square Root

PART III: APPLICATIONS

For questions 1-4, consider the following: A business purchases a piece of equipment for $30,000. After 15 years, the equipment will have to be replaced. Its value at that time is expected to be $1,500.

1. State TWO ordered pairs that relate number of years after purchase, x and value of equipment y. (0, $30,000) (15, $1500)

2. Using the two ordered pairs from #22, find the slope.

3. Write a LINEAR equation giving the value, y of the equipment in terms of x, number of years after purchase.

4. What is the value of the equipment 5 years after it is purchased?

For questions 5-6, consider the following: The total profit, P(x), in dollars for a company to manufacture and sell x items per week is given by the function, .

5. How many items should be produced each week to maximize profit?

6. What is the maximum profit earned by the company in a week?

7. Emily borrows $15,000 at an annual interest rate of 6.75%, compounded monthly. Find the balance after 7 years.

8. The antler spread a (in inches) and shoulder height h (in inches) of an adult male American elk are related by the model:

Approximate the shoulder height of a male American elk with an antler spread, a = 45 inches

PART VI: POLYNOMIAL FUNCTION: For questions 21-26, consider the following:

9. What is the degree, n, of the polynomial function? ___3__________

10. Use the Rational Root Test to list ALL possible rational zeros of the polynomial

11. Find ALL the zeros of the polynomial, real and imaginary. Write your final answer below as ordered pairs.

12. Find the y-intercept. Write final answer as an ordered pair. ____(0, -4)_____

13.

14. Is the function continuous or discontinuous? _______continuous____________

PART VII: MISCELLANEOUS

For questions 27-35, consider the following:

15. Does the given graph represent a function?

Yes

16. How do you know the given graph is a function? Passes Vertical Line Test

17. Determine the domain of the given function. Write final answer in interval notation.

18. Determine the range of the given function. Write final answer in interval notation.

19. Identify the relative minimum. Write as an ordered pair. (-1, -2)

20. Identify the relative maximum. Write as an ordered pair. (-3,2)

21. Indicate the x-intervals for which the function is increasing. Write final answer in interval notation.

22. Indicate the x-intervals for which the function is decreasing . Write final answer in interval notation. (-3,-1)

23. Does the given function have an inverse? How do you know? No, fails horizontal line test

For question 29, use properties of logarithms to condense each logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions without using calculator.

24.

For questions 30-32, solve each equation. Round answers to four decimal places as needed.

25.

26.

27.

28. Solve this equation: . Show your work.

Factor by grouping (x³ – 3x²) (-x + 3) = 0

x²(x – 3) -1(x – 3) = 0

(x – 3) (x² – 1) = 0

(x – 3) (x + 1) (x – 1) = 0

x – 3 = 0 or x + 1 = 0 or x – 1 = 0

x = 3 x = -1 x = 1

29. Part A. Graph on your calculator. Use the grid for a Cartesian coordinate plane below to show the graph of the function and to identify the x-intercept(s) and y-intercept(s).

x-intercepts (-2, 0) (1, 0)

y-intercept (0, 2)

Part B: Use the graph to help you solve the equation .

Using graph and synthetic division, “prove” that (-2, 0) and (1, 0 ) with multiplicity of 2 are the solutions.