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Find the asymptotes of the graph y = 1/(f)x.  Format your answer as follows: list the x-coordinates of any vertical asymptotes of y=1/f(x), then the righthand side of the slope-intercept form of the equation of any horizontal or oblique asymptote.  For instance, if you find y = 1/f(x) has asymptotes x = 3, x = 5, and y = −x + 2, then answer ”3,5,-x+2”.

 Jun 15, 2024
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Analyzing f(x) and Asymptotes:

 

1. Vertical Asymptotes:

 

f(x) = 0 when x = 0. Since dividing by zero is undefined, this means there's a vertical asymptote at:

 

x = 0

 

2. Horizontal Asymptotes:

 

The degree of the numerator (1) is less than the degree of the denominator (2) in f(x). Following the first case mentioned earlier:

 

The horizontal asymptote of y = 1/(f(x)) is y = 0 (the x-axis).

 

3. Oblique Asymptotes:

 

The degree of the numerator isn't one greater than the degree of the denominator. Therefore:

 

There are no oblique asymptotes.

 

In conclusion:

 

Vertical asymptote: x = 0

 

Horizontal asymptote: y = 0

 Jun 15, 2024

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