Please choose the answer and show your calculations/ explanations for each question/equation.

13. State how many imaginary and real zeros the function has. (1 point)

f(x) = x⁵+ 7x⁴+ 2x³+ 14x²+ x + 7

	3 imaginary; 2 real
	4 imaginary; 1 real
	0 imaginary; 5 real
	2 imaginary; 3 real

14.

Write a linear factorization of the function.(1 point)

f(x) = x⁴+ 16x²

	f(x) = x2(4x + i)(4x - i)
	f(x) = x2(x + 4i)2
	f(x) = x2(x + 4i)(x - 4i)
	f(x) = x2(4x + i)2

15.

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.

	-1 + i
	-i
	-1 - i
	1

16.

State the domain of the rational function. (1 point)

f(x) = 7/14-x

	All real numbers except 14
	All real numbers except -14 and 14
	All real numbers except 7
	All real numbers except -7 and 7

17.

State the vertical asymptote of the rational function.(1 point)

f(x) = (x-7)(x+4)/x²-4

	x = 2, x = -2
	None
	x = 7, x = -4
	x = -7, x = 4

18.

State the horizontal asymptote of the rational function. (1 point)

f(x) = x+9/x²+8x+5

	y = x
	y = 0
	y = 9
	None

19.

State the horizontal asymptote of the rational function. (1 point)

f(x) = x²+9x-9/x-9

	y = 3
	None
	y = 9
	y = -9

20.

Give an example of a rational function that has a horizontal asymptote of y = 2/9. (1 point)