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For what values of x, if any, does #f(x) = 1/((x-9)(x-1)(x-3)) # have vertical asymptotes?

Answer 1

x = 9 , x = 1 , x = 3

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

solve : (x-9)(x-1)(x-3) = 0 #rArr x = 9 , x = 1 " and " x = 3 #

Here is the graph of the function graph{1/((x-9)(x-1)(x-3)) [-20, 20, -10, 10]}

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Answer 2

Isabella Ackerman

The function f(x) = 1/((x-9)(x-1)(x-3)) has vertical asymptotes at x = 9, x = 1, and x = 3.

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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.