Project #161477 - math2

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 = x2

Q4. 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

Q5. 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

Q6. 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

Q7. 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. neither

Q10. 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 6

Q11. 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 5

Q12. Use the graph to find the vertical asymptotes, if any, of the function.

<b
    a. x = -3, x = 3, x = 0
    b. x = -3, x = 3, y = 0
    c. none
    d. x = -3, x = 3

Q13. Solve the inequality.

(x - 5)(x2 + x + 1) > 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; no

Q15. 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. none

Q18. 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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