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How many non-verticle asymptotes can a rational function have?
Not sure what non-verticle means, but a rational function can have up to 2 non-vertical asymptotes,
What do the asymptotes represent when you graph the tangent function?
When you graph a tangent function, the asymptotes represent x values 90 and 270.
Can a rational function have no vertical horizontal oblique asymptotes?
No, it will always have one.
Is it possible for graph of function to cross the horizontal assymptotes?
When you plot a function with asymptotes, you know that the graph cannot cross the asymptotes, because the function cannot be valid at the asymptote. (Since that is the point of having an asymptotes - it is a "disconnect" where the function is not valid - e.g when dividing by zero or something equally strange would occur). So if you graph is crossing an asymptote at any point, something's gone wrong.
A function has vertical asymptotes at x-values for which it is and near which the function's values become very positive or negative numbers?
Undefined; large
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