# How do you find the vertical, horizontal or slant asymptotes for #x/(x^2+ 5x +6)#?

vertical asymptotes x = -3 , x = -2

horizontal asymptote y = 0

Vertical asymptotes occur as the denominator of a rational function tends to zero. To find the equation/s set the denominator equal to zero.

Horizontal asymptotes occur as

Slant asymptotes occur when the degree of the numerator > degree of the denominator. This is not the case here (numerator-degree 1 , denominator-degree 2 ) Hence there are no slant asymptotes. graph{x/(x^2+5x+6) [-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 the function ( \frac{x}{x^2 + 5x + 6} ), the denominator (x^2 + 5x + 6) equals zero when (x = -2) and (x = -3). So, there are vertical asymptotes at (x = -2) and (x = -3).

To find horizontal asymptotes, compare the degrees of the numerator and the denominator. If the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is at (y = 0). If the degree of the numerator is equal to the degree of the denominator, divide the leading coefficients to find the horizontal asymptote. If the degree of the numerator is greater than the degree of the denominator, there is no horizontal asymptote.

In this case, the degree of the numerator (1) is less than the degree of the denominator (2). So, the horizontal asymptote is at (y = 0).

To find the slant (oblique) asymptote, if the degree of the numerator is exactly one more than the degree of the denominator, you can use polynomial long division to find the equation of the slant asymptote. In this case, since the degree of the numerator is less than the degree of the denominator, there is no slant asymptote.

Therefore, the vertical asymptotes are at (x = -2) and (x = -3), and the horizontal asymptote is at (y = 0). There is no slant asymptote.

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 vertical, horizontal and oblique asymptotes for # f(x) = (x^2 - 9) / (x - 4)#?
- How do you find the asymptotes for #g(x) = (4x^2+11) /( x^2+8x−9)#?
- How do you find the Vertical, Horizontal, and Oblique Asymptote given #f(x) = (2x - 3)/( x^2 - 1)#?
- How do you find the end behavior of #f(x) = -2(x-1)(x+3)^3#?
- How do you find the inverse of the function: #f(x)= 6+ sqrt(x+7)#?

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