Download Math 1113 Test 4 Practice: Graphs, Zeros, Remainders, Factors, Polynomials and more Exams Pre-Calculus in PDF only on Docsity!
ü Math 1113 Test 4 Practice Problems ü Except when instructed otherwise, please write the letter of the correct answer in the blank on the left.
- Label each of the graphs below with the letter of one of the following equations. (A) y = x I x^2 - 1 M (B) y = x^2 H x - 1 L (C) y = x H x - 1 L^3 (D) y = x H x - 1 L^2 (E) y = H x - 1 L^3 (F) y = H x + 1 L^2 x H x - 1 L (G) y = H x + 1 L x^2 H x - 1 L (H) y = x^2 H x - 1 L 2
- 1 1 2 3 - 1 1 2
- 2 - 1 1 2 - 1 1 2
- 2 - 1 1 2 __________ 2. Find all three rational zeros of 6 x^3 - 35 x^2 - 11 x + 30. What is their product? (a) 5 ê 6 (b) 1 (c) - 5 ê 3 (d) - 5 (e) 3 __________ 3. Find the remainder when x^100 + x^2 + x + 1 is divided by x - 1. (a) 4 (b) 1 (c) 0 (d) - 3 (e) 2 __________ 4. Given that x - 2 is a factor of x^4 - 2 x^3 + x^2 + x - 6 , find the other factor. (a) x^3 + x^2 + x + 3 (b) x^3 + x + 3 (c) x^3 + 3 x + 1 (d) x^3 + 2 x + 3 (e) x^3 + x^2 + 3 __________ 5. Which of the following cannot be a zero of P H x L = 6 x^5 + 7 x^3 + b x^2 + c x + 15 if b and c are integers? (a) - 3 (b) - 5 ê 2 (c) 3 ê 5 (d) 5 ê 2 (e) 15 ê 6 __________ 6. Find the cubic polynomial P H x L with zeros 1/3 and 2 Â and constant term 4. (a) - 3 x^3 + x^2 - 12 x + 4 (b) 6 x^3 + x^2 - 12 x + 4 (c) 3 x^3 - x^2 - 8 x + 4 (d) - 9 x^3 + 3 x^2 - x + 4 (e) 2 x^3 - 3 x^2 + 4 (f) - 3 x^3 + 6 x + 4
7 | 14 Match each expression on the left with a value on the right. __________ 7. ln 3 ‰ (a) - 2 __________ 8. ln I 3 ‰^2 M (b) - ln 3 __________ 9. ln 8 (c) 12 H 1 + ln 3 L __________ 10. ln 24 - ln 4 (d) ln 3 + ln 2 __________ 11. ‰^2 ln^3 (e) 2 + ln 3 __________ 12. ln ‰^3 (f) 3 __________ 13. ln 31 (g) 9 __________ 14. ln
‰^2
(h) 3 ln 2 __________ 15. Solve for x : 2 I 5 - ‰- x ê^2 M = 6. (a) - 2 ln 2 (b) 2 + ln 3 (c) - 2 ln 3 (d) - 4 (e) ln 12 __________ 16. The graph of a function of the form f H x L = a ‰ kx^ passes through the points H 0 , 10 L and H 10 , 1 L. Find k. (a) 1 ln 10 (b) 10 lnK 1 10 O (c) 10 ln 10 (d) - ln 10 10 __________ 17. If $1000 is invested in a account bearing 7% annual interest compounded continuously , how much will the account be worth after 20 years? Round to the nearest dollar. (a) $4017 (b) $7433 (c) $4055 (d) $2780 (e) $ __________ 18. Find the horizontal asymptote of the graph of f H x L = 3 x (^3) - x 2 x^3 + 3 x^2 - x + 2
(a) y = 2 ê 3 (b) y = 1 (c) y = 3 (d) y = 3 ê 2 (e) y = 0 __________ 19. Find the slant asymptote of the graph of f H x L = x (^3) - 2 x 2 2 x^2 + 8 x + 1
(a) y = 12 x (b) y = 12 x - 3 (c) y = 2 x (d) y = x - 4 (e) y = x + 2 __________ 20. Which of these rational functions has no vertical asymptote? (a) x x^2 + 2 (b) x^ -^3 x^3 + 2 (c) 1 x^2 + x - 2 (d) 1 x^4 + x^2 (e) x 1 + x
