Math 1314 College Algebra (INET)

# Math 1314 College Algebra (INET)

## Unit 3 Test – Chapter 5

### To earn full credit on all questions you MUST do the following.

For Questions 1 and 2, use the given polynomial to answer the following questions.

1. Classify the polynomial as linear, quadratic, cubic, or quartic. Then determine the leading term.

2. Determine the leading coefficient and the degree of the polynomial.

3. What is the end behavior for each polynomial function.

a.

b.

4. Use the given function to answer the following questions.

a. Does have a maximum or minimum value?

b. What is the maximum or minimum value?

5. Graph the function . Be sure to find the following:

a. Vertex

b. Axis of symmetry

c. Maximum or minimum value

d. X and y-intercepts

e. Domain and range

6. The function    represents the yearly income (or loss) from a real estate investment, where t is time in years. After what year does income begin to decline?

7. The polynomial   gives the approximate total earnings of a company, in millions of dollars, where x represents the number of years since 1996 . This model is valid for the years from 1996 to 2000. Determine the earnings for 2000. Round your answer to two decimals, if necessary.

8. A projectile is thrown upward so that its distance above the ground after t seconds is .  After how many second does it reach its maximum height?

9. Use synthetic division to find the quotient and the remainder when is divided by . Express your answer in the factored form

.

10. Find a polynomial of degree 4 with -3 as a zero of multiplicity 2, -2 as a zero of multiplicity 1, and -1 as a zero of multiplicity 1. State your answer in factored form.

11. Find a polynomial function of degree 3 with zeros at 5 and 2i. Multiply all linear factors.

12. Use algebraic techniques to sketch the function: Clearly indicate the following:

a. Zeros

b. Y-intercept

c. End behavior

13. List all possible rational zeros for the polynomial.

14. Find all zeros for the given function. You must solve algebracially using techniques shown in the textbook.

15. Use the given function to answer the following questions.

a. State the domain of the function using interval notation.

b. State the equation of the vertical asymptote(s).

c. State the equation of the horizontal asymptote.

16. Use the given function to answer the following questions.

a. State the domain of the function using interval notation.

b. State the horizontal asymptote

17. Use the given function to answer the following questions.

a. State the domain of the function using interval notation.

b. State the hole and/or vertical asymptotes

18. Graph the function . Clearly indicate the x and y-intercepts and show all asymptotes as dashed lines.