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If a hyperbola is vertical, the asymptotes have a slope of m = +- a/b. If a hyperbola is horizontal, the asymptotes have a slope of m = +- b/a.
When you graph a tangent function, the asymptotes represent x values 90 and 270.
Not sure what non-verticle means, but a rational function can have up to 2 non-vertical asymptotes,
denominators
No, it will always have one.