# How do you find the vertical, horizontal and slant asymptotes of: #f(x)= (4x^2+ 4x-24)/(x^4- 2x^3 - 9x^2+ 18x)#?

The numerator factors like this:

The denominator factors like this:

graph{(4x^2+4x-24)/(x^4-2x^3-9x^2+18x) [-10, 10, -5, 5]}

By signing up, you agree to our Terms of Service and Privacy Policy

To find the vertical asymptotes, set the denominator equal to zero and solve for ( x ). For horizontal asymptotes, compare the degrees of the numerator and denominator. If the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is ( y = 0 ). If the degrees are equal, divide the leading coefficients of the numerator and denominator to find the horizontal asymptote. If the degree of the numerator is greater, there is no horizontal asymptote. To find slant asymptotes, perform polynomial long division and the slant asymptote is the quotient.

By signing up, you agree to our Terms of Service and Privacy Policy

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- How do you find the asymptotes for #(2x^2)/((-3x-1)^2)#?
- If f(x) = 7-2x and g(x) = x+3 . A. What is g^-1 (x) ? B. What is f(g^-1(5)) ?
- How do you find the asymptotes for #f(x)= -1/(x+1)^2#?
- How do you find the inverse of #f(x) = x / (x + 8)#?
- How do you determine whether a function is odd, even, or neither: #f(x)=2x^4-x^2#?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7