+22 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”.
+461 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
