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# A DEVELOPER WANTS TO ENCLOSE A RECTANGULAR GRASSY LOT THAT BORDERS A CITY STREET FOR PARKING.

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Quiz 3Q1. A developer wants to enclose a rectangular grassy lot that borders a city street forparking. If the developer has 320 feet of fencing and does not fence the side along thestreet, what is the largest area that can be enclosed?a. 25,600 ft2b. 19,200 ft2c. 12,800 ft2d. 6400 ft2Q2. Solve the equation in the real number system.x3 + 9x2 + 26x + 24 = 0a. {-4, -2, -3}b. {2, 4}c. {3, 2, 4}d. {-4, -2}Q3. Find the indicated intercept(s) of the graph of the function.y-intercept of f(x) =a. (0, 3)b. (0, 4)c.d.Q4. Use the intermediate value theorem to determine whether the polynomial function hasa zero in the given interval.f(x) = -2x4 + 2x2 + 4; [-2, -1]a. f(-2) = 20 and f(-1) = 5; nob. f(-2) = -20 and f(-1) = 4; yes c. f(-2) = 20 and f(-1) = -4; yesd. f(-2) = -20 and f(-1) = -4; noQ5. Determine, without graphing, whether the given quadratic function has a maximumvalue or a minimum value and then find that value.f(x) = -x2 - 2x + 2a. minimum; - 1b. maximum; 3c. minimum; 3d. maximum; - 1Q6. Determine, without graphing, whether the given quadratic function has a maximumvalue or a minimum value and then find that value.f(x) = x2 - 2x - 5a. maximum; 1b. minimum; 1c. maximum; - 6d. minimum; - 6Q7. Solve the inequality.(x - 5)(x2 + x + 1) > 0a. (-∞, -1) or (1, ∞)b. (-1, 1)c. (-∞, 5)d. (5, ∞)Q8. 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 origin b. symmetry with respect to the y-axisc. neitherQ9. Solve the equation in the real number system.x4 - 3x3 + 5x2 - x - 10 = 0a. {-1, -2}b. {1, 2}c. {-1, 2}d. {-2, 1}Q10. Find all of the real zeros of the polynomial function, then use the real zeros to factor fover the real numbers.f(x) = 3x4 - 6x3 + 4x2 - 2x + 1a. no real roots; f(x) = (x2 + 1)(3x2 + 1)b. 1, multiplicity 2; f(x) = (x - 1)2(3x2 + 1)c. -1, 1; f(x) = (x - 1)(x + 1)(3x2 + 1)d. -1, multiplicity 2; f(x) = (x + 1)2(3x2 + 1)Q11. Use the Theorem for bounds on zeros to find a bound on the real zeros of thepolynomial function.f(x) = x4 + 2x2 - 3a. -4 and 4b. -3 and 3c. -6 and 6d. -5 and 5Q12. Use the Factor Theorem to determine whether x - c is a factor of f(x).8x3 + 36x2 - 19x - 5; x + 5a. Yesb. NoQ13. Find the power function that the graph of f resembles for large values of |x|. f(x) = (x + 5)2a. y = x10b. y = x25c. y = x2d. y = x5Q14. Find the domain of the rational function.f(x) =.a. {x|x ≠ -3, x ≠ 5}b. {x|x ≠ 3, x ≠ -5}c. all real numbersd. {x|x ≠ 3, x ≠ -3, x ≠ -5}Q15. State whether the function is a polynomial function or not. If it is, give its degree. If itis not, tell why not.f(x) = 9x3 + 8x2 - 6a. No; the last term has no variableb. Yes; degree 5c. Yes; degree 3d. Yes; degree 6Q16. Give the equation of the oblique asymptote, if any, of the function.h(x) =a. y = 4xb. y = 4c. y = x + 4d. no oblique asymptote Q17. Find all zeros of the function and write the polynomial as a product of linear factors.f(x) = 3x4 + 4x3 + 13x2 + 16x + 4a. 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)Q18. Use the graph to find the vertical asymptotes, if any, of the function.a. x = -3, x = 3, x = 0b. x = -3, x = 3, y = 0c. noned. x = -3, x = 3Q19. Find the indicated intercept(s) of the graph of the function.x-intercepts of f(x) =a. (5, 0)b.c.d. (-5, 0) Q20. Find k such that f(x) = x4 + kx3 + 2 has the factor x + 1.a. -3b. -2c. 3d. 2

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