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

Answer 1

Vertical asymptote is x=7 and
Horizontal asymptote is y=0, that is x axis

f(x)= #(x+7)/(x^2-49)= 1/(x-7)#

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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Answer 2

Sophie Adams

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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Answer from HIX Tutor

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.