Find a rational function

Question

Hi, I am trying to find a rational function based on characteristics:

vertical asymptote x=0

horizontal asymptote y=0

no slant

x intercepts at 5/2

y intercepts never cross

no end behavior negative infinity, 0, infinity, 0

Answer 1

1. If 5/2 is the x-intercept. then (x-5/2) is a factor of the numerator
2. Since there is a vertical asymptote at x= 0, there must be a factor of x in the denominator.
3. Since there is a horizontal asymptote at y=0, the degree of the denominator must be greater than the degree of the numerator, so try x² in the denominator,
4. Since a vertical asymptote is never crossed by the graph, this graph never touches the y-axis.

Check out this graph for a possible answer and confirmation:

desmos.com/calculator/b8o8qeus7u