How do you find all the asymptotes for function #y=1/x#?

Answer 1

Asymptotes are where the function basically has a vertical "no crossing", "restricted" line. Generally, no part of the function should cross an asymptote.

You cannot divide by #0#, so #1/0# describes a vertical asymptote at #x = 0#. Also, #0 ne 1/x# because #x*0 = 0 ne 1#, so there is a horizontal asymptote at #y = 0#.

graph{1/x [-10, 10, -5, 5]}

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Answer 2

Serenity Jones

To find the asymptotes for the function ( y = \frac{1}{x} ), we need to consider both vertical and horizontal asymptotes.

Vertical asymptotes occur where the denominator of the function approaches zero while the numerator remains non-zero. For ( y = \frac{1}{x} ), the vertical asymptote occurs at ( x = 0 ).

Horizontal asymptotes occur as ( x ) approaches positive or negative infinity. For ( y = \frac{1}{x} ), there is a horizontal asymptote at ( y = 0 ).

Therefore, the asymptotes for the function ( y = \frac{1}{x} ) are:

Vertical asymptote: ( x = 0 )
Horizontal asymptote: ( y = 0 ).

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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.