Use the function to answer the following questions fx x3 7x

Use the function to answer the following questions. f(x) = x^3 -7x - 6/12x^4 + 32x^3 - 33x^2 - 83x + 30 What is the degree of the numerator? What are the zeros of the numerator? What are the factors of the numerator? What is the degree of the denominator? What are the zeros of the denominator? What are the factors of the denominator? What is the factored form of the rational function? Does the function have any vertical asymptotes; if so, where? Does the function have a horizontal asymptote? Does the function have an oblique asymptote? What is the equation of the horizontal/oblique asymptote(s)? Does the function have any holes; if so, where? Over what intervals is f(x) > 0 ? Over what intervals is f(x)

Solution

1. Degree of Numerator= 3

2. Zeros of Numerator= -2, -1 and 3

3. Factors of numeratoro= (x-3)(x+1)(x+2)

4. Degree of Denominator = 4

5. Zeros of denominator = -5/2, -2, 1/3, 3/2

6. Factors of denominator = (x+2)(2x-3)(2x+5)(3x-1)

7. Factored form of rational function is

f(x)=[(x-3)(x+1)]/[(2x-3)(2x+5)(3x-1)]