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Factoring is usually helpful in identifying zeros of denominators.
If there are not common factors in the numerator and the denominator, the lines x equal the zeros of the denominator are the vertical asymptotes for the graph of the rational function.
Example:
f(x) = x/(x^2 - 1)
f(x) = x/[(x + 1)(x - 1)]
x + 1 = 0 or x - 1 = 0
x = -1 or x = 1
Thus, the lines x = -1 and x = 1 are the vertical asymptotes of f.
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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,
How many asymptotes can a bounded function have?
I believe the maximum would be two - one when the independent variable tends toward minus infinity, and one when it tends toward plus infinity. Unbounded functions can have lots of asymptotes; for example the periodic tangent function.
How many asymptotes does a hyperbola have?
A hyperbola has 2 asymptotes.www.2dcurves.com/conicsection/​conicsectionh.html
What slope does a vertical line have?
In terms of the slope intercept form of the line, it is undefined. A vertical line is not a function since a single value of x is mapped onto infinitely many y values.
Is the set of rational numbers finite?
No; there are infinitely many rational numbers.
