# How do you find the vertical, horizontal or slant asymptotes for #1/(x^2+4)#?

horizontal asymptote : y=0

vertical asymptote : none

slant asymptote : none

because the numerator is of lower degree than the denominator then there are no slant asymptotes and the horizontal asymptote is :

y=0

to find the vertical asymptote you put the denominator= 0

you can see that it has no real solutions so there are no vertical asymptotes of this rational function

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

The denominator of f(x) cannot be zero as this would make f(x) undefined. Equating the denominator to zero and solving gives the values that x cannot be and if the numerator is non-zero for there values then they are vertical asymptotes.

This has no real solutions, hence there are no vertical asymptotes.

Horizontal asymptotes occur as

Slant asymptotes occur when the degree of the numerator > degree of the denominator. This is not the case here, hence there are no slant asymptotes. graph{1/(x^2+4) [-10, 10, -5, 5]}

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

For the function ( \frac{1}{x^2 + 4} ), there are no vertical asymptotes. There are horizontal and slant (or oblique) asymptotes.

To find the horizontal asymptote:

- As ( x ) approaches positive or negative infinity, the function ( \frac{1}{x^2 + 4} ) approaches 0. Hence, the horizontal asymptote is ( y = 0 ).

To find the slant asymptote (if it exists):

- Divide the numerator by the denominator using long division or polynomial division. Here, we have: [ \frac{1}{x^2 + 4} = \frac{0}{x^2} + \frac{1}{x^2 + 4} ]
- The quotient is ( 0 ) and the remainder is ( \frac{1}{x^2 + 4} ).
- Since the degree of the numerator is less than the degree of the denominator, the slant asymptote does not exist.

Therefore, for ( \frac{1}{x^2 + 4} ):

- There is a horizontal asymptote at ( y = 0 ).
- There is no vertical asymptote.
- There is no slant (or oblique) asymptote.

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

- What is the inverse function of #f(x)= (3x-2)/(x+7)?
- How do you find the vertical, horizontal or slant asymptotes for #y = (2e^x) / (e^x - 5)#?
- How do you find the domain and range and is it a function given points #{(4,-2), (4,2), (1,-1), (1,1), (0,0)}#?
- How do you find vertical, horizontal and oblique asymptotes for #-7 / (x+4)#?
- How do you find vertical, horizontal and oblique asymptotes for # (2x+sqrt(4-x^2)) / (3x^2-x-2)#?

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