# MTH1014 Quiz 6Spring 2013

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This is quiz 6 to be taken by Friday, 5 April 2013. It should take you between an hour and 4hours to answer the following questions. You should do this quiz after doing the rest of assignment 6'. Because this was a double assignment, this is a double quiz, worth 2 ordinary quizzes.

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Please answer the following questions on this form (or on a paper copy of this form).

1. Carefully, and in detail with examples, explain what a polynomial function is and what the degree of a plynomial function is.

2. Carefully, and in detail with examples, but only using words, not pictures, explain how to identify the zeros of a polynomial that you can factor completely and how to determine the degree of each of those zeros.

3. Expain what what impact the multiplicity of a zero has on the graph of a polynimial function at that zero.

4. How many turning points, at most, can polynomial functions of the following degrees have: 1, 2, 3, 4, 100, 100000001?

5. Carefully and in detail with examples, explain how to determine the domain of a rational function and the vertical asymptotes of a rational function.

6. Carefully and in detail, explain how to find the horizontal or oblique asymptotes of a rational function.

7. Carefully and in detail, with a worked example, explain what it means to write a rational function in lowest terms.

8. Using any appropriate tools -- a graphing calculator, a computer, a piece of scrap graph paper, solve 6*x2+3*x-12 < 0. Give the answer in interval notation.

9. Using any appropriate tools -- a graphing calculator, a computer, a piece of scrap graph paper, solve (6*x2+3*x-12)/(2*x^2 -1) < 0.

10. Carefully state the division theorem for polynomials.

11. Carefully state Descartes' Rule of Signs.

12. Carefully state the Rational Zeros Theorem.

13. Carefully state the Theorem for the Bounds on Zeros.

14. Carefully state the Intermediate Value Theorem.

15. Carefully explain how to locate real zeros using the Intermediate Value Theorem. Note -- if you go into applied math, this is the most important thing you will learn in this course.

16. Carefully state the Fundamental Theorem of Algebra and use it to explain the number of linear factors of a complex polynomial of degree n.

17. Carefully, using words, not pictures, and giving a worked example, explain how to find the domain of a composite function.

18. Carefully, using words, not pictures, and giving a worked example, explain what it means for a function to be 1-1 and how that relates to finding the inverse of a function

19. Carefully, using words, not pictures, and giving a worked example, explain what an exponential function, f(x), is and how it behaves as x goes to +infinity and how it behaves as x goes to -infinity. Be careful in answering this. You will get no credit unless your answer in the behavior going to +/- infinity is complete.

20. Carefully and in detail, using words, not pictures, explain the relationships among exp(x), 10x, log10(x) and ln(x)

21. Carefully and in detail, using words and formulae, not pictures, explain the relationships among simple interest, compound interest and continously compounded interest. Be careful to give the formula for each, explaining each symbol you use.

22. If you invest \$100 with a bank that has promised to pay you 3% interest per annum compounded continuously, how much mony money will you have after 1 year, after 10 years, after 20 years and after 40 years. Redo the problem for 11% interest.

23. You start with 1 pound of cesium-137 in 2012. You know that the amount of cesium-137 will decay exponentially following the law of uninhibited decay, and that the half-life of cesium-137 is 30.17 years. How long will it take for there to be less than 1/16,384 of a pound of cesium-137 left in your original pound of material?

<==== Do this AFTER you''ve answered all the questions

You probably DON'T want to do this ===>

Revised 4 April 2013