# Mathematics Tutors

 Subject Mathematics Due By (Pacific Time) 12/26/2016 12:00 am

 Q1. Find all zeros of the function and write the polynomial as a product of linear factors.f(x) = 3x4 + 4x3 + 13x2 + 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)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. 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 = x2Q4. 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; - 6Q5. 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; - 1Q6. 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 1Q7. Solve the equation in the real number system.x3 + 9x2 + 26x + 24 = 0    a. {-4, -2, -3}    b. {2, 4}    c. {3, 2, 4}    d. {-4, -2}Q8. Solve the equation in the real number system.x4 - 3x3 + 5x2 - x - 10 = 0    a. {-1, -2}    b. {1, 2}    c. {-1, 2}    d. {-2, 1}Q9. 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. neitherQ10. 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) = 9x3 + 8x2 - 6    a. No; the last term has no variable    b. Yes; degree 5    c. Yes; degree 3    d. Yes; degree 6Q11. Use the Theorem for bounds on zeros to find a bound on the real zeros of the polynomial function.f(x) = x4 + 2x2 - 3    a. -4 and 4    b. -3 and 3    c. -6 and 6    d. -5 and 5Q12. Use the graph to find the vertical asymptotes, if any, of the function. 0    a. (-∞, -1) or (1, ∞)    b. (-1, 1)    c. (-∞, 5)    d. (5, ∞)Q14. Use the intermediate value theorem to determine whether the polynomial function has a zero in the given interval.f(x) = 8x3 - 10x2 + 3x + 5; [-1, 0]    a. f(-1) = -16 and f(0) = -5; no    b. f(-1) = -16 and f(0) = 5; yes    c. f(-1) = 16 and f(0) = -5; yes    d. f(-1) = 16 and f(0) = 5; noQ15. Find all of the real zeros of the polynomial function, then use the real zeros to factor f over the real numbers.f(x) = 3x4 - 6x3 + 4x2 - 2x + 1    a. 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)Q16. Determine, without graphing, whether the given quadratic function has a maximum value or a minimum value and then find that value.f(x) = 2x2 - 2x    a. minimum; -    b. minimum;      c. maximum; -    d. maximum;  Q17. Use the graph to find the vertical asymptotes, if any, of the function.    a. y = 0    b. x = 0, y = 0    c. x = 0    d. noneQ18. 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}Q19. Find the indicated intercept(s) of the graph of the function.y-intercept of f(x) =      a. (0, 3)    b. (0, 4)    c.     d. Q20. 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-axis    c. neither

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