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Mathematics, 09.10.2019 03:00 ashhleyjohnson
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.
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