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Does every rational function have an asymptote?
No if the denominators cancel each other out there is no asymptote
Does y equals log5x have an asymptote?
Yes, the asymptote is x = 0. In order for logarithmic equation to have an asymptote, the value inside log must be 0. Then, 5x = 0 → x = 0.
How do you find the horizontal asymptote in a graph of a rational function?
The horizontal asymptote is what happens when x really large. To start with get rid of all the variables except the ones with the biggest exponents. When x is really large, they are the only ones that will matter. If the remaining exponents are the same, then the ratio of those coefficients tell you where the horizontal asymptote is. For example if you have 2x3/3x3, then the ratio is 2/3 and the asymptote is f(x)=2/3 or y=2/3. If the exponent in the denominator is bigger, than y=0 is the horizontal asymptote. If the exponent in the numerator is bigger, than there is no horizontal asymptote.
Can the graph of a polynomial function have a vertical asymptote?
no
How do you find vertical asymptote?
One way to find a vertical asymptote is to take the inverse of the given function and evaluate its limit as x tends to infinity.
