Finding a function given its limits

Hello everyone,

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lim x-->0 (f(x))=0, x<0

lim x-->0 ( f(x))=infinity, x>0

From this information, I was able to deduce that the y axis is a vertical asymptote to the function. However, I could not find the equation of the function. I thought about functions with absolute values, logarithmic, rational, exponential, and irrational functions; however, nothing seemed to work. Could you please help me with this?

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PS: I cannot use a piecewise function!