Horizontal Asymptote y=0 and a Vertical Asymptote at x = 0
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A function with a horizontal asymptote of y=0 and a vertical asymptote at x=0 would look something like this:
f(x) = k/x
Where k is a nonzero constant.
To understand why this function has a horizontal asymptote of y=0, we can use the idea of limits. As x approaches infinity or negative infinity, the denominator of the fraction becomes very large or very small, respectively. This means that the overall value of the fraction approaches 0. Therefore, as x approaches infinity or negative infinity, the function approaches y=0.
To understand why this function has a vertical asymptote at x=0, we can again use the idea of limits. As x approaches 0 from the left or the right, the denominator of the fraction approaches 0. This means that the overall value of the fraction becomes very large, approaching positive or negative infinity depending on the direction of approach. Therefore, as x approaches 0 from either side, the function approaches infinity or negative infinity.
So, in summary, a function with a horizontal asymptote of y=0 and a vertical asymptote at x=0 is of the form f(x) = k/x, where k is a nonzero constant.
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