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For what values of x, if any, does #f(x) = 1/((x+3)(x-2)) # have vertical asymptotes?

Answer 1

vertical asymptotes are x = -3 and x = 2

Vertical asymptotes occur as the denominator of a rational function tends to zero. To find the equation/s set the denominator equal to zero.

solve : (x+3)(x-2) = 0 → x = -3 , x = 2

#rArr x = -3" and " x = 2" are the asymptotes " # graph{1/((x+3)(x-2)) [-10, 10, -5, 5]}

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Answer 2

Charles Arocha

The function f(x) = 1/((x+3)(x-2)) has vertical asymptotes at x = -3 and x = 2.

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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.