Q1. Determine, without graphing, whether the given quadratic function has a maximum value or a minimum value and then find that value. f(x) = x2 – 2x – 5 a. maximum; 1 b. minimum; 1 c. maximum; – 6 d. minimum; – 6 Q2. Find the domain of the rational function. g(x) = a. all real numbers b. {x|x ≠ -7, x ≠ 7, x ≠ -5} c. {x|x ≠ -7, x ≠ 7} d. {x|x ≠ 0, x ≠ -49} Q3. Solve the inequality. (x – 5)(x2 + x + 1) > 0 a. (-∞, -1) or (1, ∞) b. (-1, 1) c. (-∞, 5) d. (5, ∞) Q4. Find the domain of the rational function. f(x) =
a. {x|x ≠ -3, x ≠ 5} b. {x|x ≠ 3, x ≠ -5} c. all real numbers d. {x|x ≠ 3, x ≠ -3, x ≠ -5} Q5. Solve the equation in the real number system. x3 + 9×2 + 26x + 24 = 0 a. {-4, -2, -3} b. {2, 4} c. {3, 2, 4} d. {-4, -2} Q6. Find k such that f(x) = x4 + kx3 + 2 has the factor x + 1. a. -3 b. -2 c. 3 d. 2 Q7. Use the Theorem for bounds on zeros to find a bound on the real zeros of the polynomial function. f(x) = x4 + 2×2 – 3 a. -4 and 4 b. -3 and 3 c. -6 and 6 d. -5 and 5 Q8. Find all zeros of the function and write the polynomial as a product of linear factors. f(x) = 3×4 + 4×3 + 13×2 + 16x + 4 a. f(x) = (3x – 1)(x – 1)(x + 2)(x – 2) b. f(x) = (3x + 1)(x + 1)(x + 2i)(x – 2i) c. f(x) = (3x – 1)(x – 1)(x + 2i)(x – 2i) d. f(x) = (3x + 1)(x + 1)(x + 2)(x – 2) Q9. Find the power function that the graph of f resembles for large values of |x|. f(x) = -x2(x + 4)3(x2 – 1) a. y = x7 b. y = -x7 c. y = x3 d. y = x2 Q10. Use the Factor Theorem to determine whether x – c is a factor of f(x). 8×3 + 36×2 – 19x – 5; x + 5 a. Yes b. No Q11. State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not. f(x) = 9×3 + 8×2 – 6 a. No; the last term has no variable b. Yes; degree 5 c. Yes; degree 3 d. Yes; degree 6 Q12. Solve the equation in the real number system. x4 – 3×3 + 5×2 – x – 10 = 0 a. {-1, -2} b. {1, 2} c. {-1, 2} d. {-2, 1} Q13. A developer wants to enclose a rectangular grassy lot that borders a city street for parking. If the developer has 320 feet of fencing and does not fence the side along the street, what is the largest area that can be enclosed? a. 25,600 ft2 b. 19,200 ft2 c. 12,800 ft2 d. 6400 ft2 Q14. State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not. f(x) =
a. Yes; degree 3 b. No; x is a negative term c. No; it is a ratio d. Yes; degree 1 Q15. Give the equation of the oblique asymptote, if any, of the function. h(x) =
a. y = 4x b. y = 4 c. y = x + 4 d. no oblique asymptote Q16. Find all of the real zeros of the polynomial function, then use the real zeros to factor f over the real numbers. f(x) = 3×4 – 6×3 + 4×2 – 2x + 1 a. no real roots; f(x) = (x2 + 1)(3×2 + 1) b. 1, multiplicity 2; f(x) = (x – 1)2(3×2 + 1) c. -1, 1; f(x) = (x – 1)(x + 1)(3×2 + 1) d. -1, multiplicity 2; f(x) = (x + 1)2(3×2 + 1) Q17. Determine whether the rational function has symmetry with respect to the origin, symmetry with respect to the y-axis, or neither. f(x) =
a. symmetry with respect to the y-axis b. symmetry with respect to the origin c. neither Q18. Find the vertex and axis of symmetry of the graph of the function. f(x) = -3×2 – 6x – 2 a. (-1, 1) ; x = -1 b. (2, -26) ; x = 2 c. (1, -11) ; x = 1 d. (-2, -8) ; x = -2 Q19. Find the indicated intercept(s) of the graph of the function.
Q20. Determine, without graphing, whether the given quadratic function has a maximum value or a minimum value and then find that value. f(x) = -x2 – 2x + 2 a. minimum; – 1 b. maximum; 3 c. minimum; 3 d. maximum; – 1
Q1. The logistic growth function f(t) = describes the population of a species of butterflies tmonths after they are introduced to a non-threatening habitat. How many butterflies are expected in the habitat after 12 months? a. 480 butterflies b. 401 butterflies c. 244 butterflies d. 4800 butterflies Q2. Find the present value. Round to the nearest cent. To get $10,000 after 2 years at 18% compounded monthly a. $5000.00 b. $6995.44 c. $8363.87 d. $11,956.18 Q3. A local bank advertises that it pays interest on savings accounts at the rate of 3% compounded monthly. Find the effective rate. Round answer to two decimal places. a. 3.44% b. 3.40% c. 36% d. 3.04% Q4. The half-life of silicon-32 is 710 years. If 100 grams is present now, how much will be present in 600 years? (Round your answer to three decimal places.) a. 0 b. 0.286 c. 94.311 d. 55.668 Q5. A fossilized leaf contains 12% of its normal amount of carbon 14. How old is the fossil (to the nearest year)? Use 5600 years as the half-life of carbon 14. a. 1031 b. 17,099 c. 20,040 d. 36,108 Q6. pH = -log10[H+] Find the [H+] if the pH = 8.4. a. 3.98 x 10-8 b. 2.51 x 10-8 c. 3.98 x 10-9 d. 2.51 x 10-9 Q7. Express y as a function of x. The constant C is a positive number. ln y = ln 4x + ln C a. y = 4Cx b. y = 4x + C c. y = (4x)C d. y = x + 4C Q8. Express as a single logarithm.
Q9. Find the amount that results from the investment. $480 invested at 16% compounded quarterly after a period of 4 years a. $864.45 b. $419.03 c. $869.11 d. $899.03 Q10. What principal invested at 8% compounded continuously for 4 years will yield $1190? Round the answer to two decimal places. a. $864.12 b. $1188.62 c. $1638.78 d. $627.48 Q11. Change the exponential expression to an equivalent expression involving a logarithm. 5x = 125 a. log125 x = 5 b. log5 125 = x c. log125 5 = x d. logx 125 = 5 Q12. Find functions f and g so that the composition of f and g is H. H(x) = |4 – 3×2| a. f(x) = x2 ; g(x) = 4 – 3|x| b. f(x) = 4 – 3|x|; g(x) = x2 c. f(x) = |x|; g(x) = 4 – 3×2 d. f(x) = 4 – 3×2 ; g(x) = |x| Q13. The half-life of plutonium-234 is 9 hours. If 70 milligrams is present now, how much will be present in 6 days? (Round your answer to three decimal places.) a. 0.689 b. 44.096 c. 0.001 d. 23.091 Q14. Solve the equation. log327 = x a. {81} b. {9} c. {3} d. {30} Q15. The function f(x) = 300(0.5) x/60 models the amount in pounds of a particular radioactive material stored in a concrete vault, where x is the number of years since the material was put into the vault. Find the amount of radioactive material in the vault after 170 years. Round to the nearest whole number. a. 425 pounds b. 42 pounds c. 235 pounds d. 53 pounds
Q16. Change the logarithmic expression to an equivalent expression involving an exponent. Q17. The function f is one-to-one. Find its inverse.
Q18. If the following defines a one-to-one function, find the inverse. {(6, 6), (12, 7), (10, 8), (8, 9)} a. {(7, 6), (9, 10), (6, 10), (7, 8)} b. {(7, 6), (6, 10), (6, 12), (7, 8)} c. Not a one-to-one function d. {(6, 6), (7, 12), (8, 10), (9, 8)} Q19. Change the exponential expression to an equivalent expression involving a logarithm. ex = 25 a. log 25 x = e b. log x e = 25 c. ln x = 25 d. ln 25 = x Q20. Express as a single logarithm. 3log6x + 5log6(x – 6) a. log6x3(x – 6)5 b. log6x(x – 6)15 c. log6x(x – 6) d. 15 log6x(x – 6)
