# How to find the asymptotes of #f(x) = (x+1) / (x^2 +3x - 4)# ?

vertical asymptotes x = -4 , x = 1

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

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To find the asymptotes of the function ( f(x) = \frac{x + 1}{x^2 + 3x - 4} ), follow these steps:

- Determine the vertical asymptotes by identifying the values of ( x ) for which the denominator is equal to zero.
- Determine the horizontal asymptote by comparing the degrees of the numerator and the denominator of the rational function.

Vertical asymptotes occur at the values of ( x ) where the denominator ( x^2 + 3x - 4 ) equals zero. Solve ( x^2 + 3x - 4 = 0 ) to find these values.

Horizontal asymptotes can be determined by comparing 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.

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