# How do you find the asymptotes for #f(x)=(x+7)/(x^2-49)#?

Vertical asymptote is x=7 and

Horizontal asymptote is y=0, that is x axis

There is a vertical asymptote given by x-7=0 that is x=7.

Further, since the degree of the polynomial in the numerator is less than the degree of the polynomial in the denominator, there would be a horizontal asymptote y=0

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To find the asymptotes for (f(x) = \frac{x+7}{x^2-49}), we first factorize the denominator:

[ f(x) = \frac{x+7}{(x+7)(x-7)} ]

Since there is a common factor of (x+7) in the numerator and denominator, we can simplify the function:

[ f(x) = \frac{1}{x-7} ]

The vertical asymptote occurs where the denominator equals zero, so (x-7 = 0) or (x = 7). Therefore, the function has a vertical asymptote at (x = 7).

There are no horizontal or slant asymptotes because the degree of the numerator is less than the degree of the denominator by more than one.

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