1. Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form. (1 point)
4, -14, and 5 + 8i


a) f(x) = x4 - 362.5x2 + 1450x - 4984
b) f(x) = x4 - 9x3 + 32x2 - 725x + 4984
c) f(x) = x4 - 67x2 + 1450x - 4984
d) f(x) = x4 - 9x3 - 32x2 + 725x - 4984

2. State how many imaginary and real zeros the function has. (1 point)
f(x) = x5 + 7x4 + 2x3 + 14x2 + x + 7


a) 3 imaginary; 2 real
b) 4 imaginary; 1 real
c) 0 imaginary; 5 real
d) 2 imaginary; 3 real

3. Write a linear factorization of the function.(1 point)
f(x) = x4 + 16x2


a) f(x) = x2 (4x + i)(4x - i)
b) f(x) = x2 (x + 4i)2
c) f(x) = x2 (x + 4i)(x - 4i)
d) f(x) = x2 (4x + i)2

4. Using the given zero, find one other zero of f(x). (1 point)
i is a zero of f(x).= x4 - 2x3 + 38x2 - 2x + 37.


a) -1 + i
b) -i
c) -1 - i
d) 1

5. State the domain of the rational function. (1 point)
f(x) = seven divided by quantity fourteen minus x.


a) All real numbers except 14
b) All real numbers except -14 and 14
c) All real numbers except 7
d) All real numbers except -7 and 7

6. State the vertical asymptote of the rational function.(1 point)
f(x) = quantity x minus seven times quantity x plus four divided by quantity x squared minus four.


a) x = 2, x = -2
b) None
c) x = 7, x = -4
d)x = -7, x = 4

7. State the horizontal asymptote of the rational function. (1 point)
f(x) = quantity x plus nine divided by quantity x squared plus eight x plus five.


a) y = x
b) y = 0
c) y = 9
d) None

8. State the horizontal asymptote of the rational function. (1 point)
f(x) = quantity x squared plus nine x minus nine divided by quantity x minus nine.


a) y = 3
b) None
c) y = 9
d) y = -9

9. Give an example of a rational function that has a horizontal asymptote of y = 2/9.