For what values of x, if any, does #f(x) = 1/((x+8)(x-7)) # have vertical asymptotes?

Answer 1

#"vertical asymptotes at "x=-8" and "x=7#

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 these values then they are vertical asymptotes.

#"solve "(x+8)(x-7)=0#
#x=-8" and "x=7" are the asymptotes"# graph{1/((x+8)(x-7) [-10, 10, -5, 5]}
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Answer 2

The function f(x) = 1/((x+8)(x-7)) has vertical asymptotes at x = -8 and x = 7.

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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.

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.

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