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No, it will always have one.

Q: Can a rational function have no vertical horizontal oblique asymptotes?

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Not sure what non-verticle means, but a rational function can have up to 2 non-vertical asymptotes,

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.

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.

Definition: If lim x->a^(+/-) f(x) = +/- Infinity, then we say x=a is a vertical asymptote. If lim x->+/- Infinity f(x) = a, then we say f(x) have a horizontal asymptote at a If l(x) is a linear function such that lim x->+/- Infinity f(x)-l(x) = 0, then we say l(x) is a slanted asymptote. As you might notice, there is no generic method of finding asymptotes. Rational functions are really nice, and the non-permissible values are likely vertical asymptotes. Horizontal asymptotes should be easiest to approach, simply take limit at +/- Infinity Vertical Asymptote just find non-permissible values, and take limits towards it to check Slanted, most likely is educated guesses. If you get f(x) = some infinite sum, there is no reason why we should be able to to find an asymptote of it with out simplify and comparison etc.

Undefined; large

Related questions

Not sure what non-verticle means, but a rational function can have up to 2 non-vertical asymptotes,

Three types of asymptotes are oblique/slant, horizontal, and vertical

finding vertical asymptotes is easy. lets use the equation y = (2x-2)/((x^2)-2x-3) since its a rational equation, all we have to do to find the vertical asymptotes is find the values at which the denominator would be equal to 0. since this makes it an undefined equation, that is where the asymptotes are. for this equation, -1 and 3 are the answers for the vertical ayspmtotes. the horizontal asymptotes are a lot more tricky. to solve them, simplify the equation if it is in factored form, then divide all terms both in the numerator and denominator with the term with the highest degree. so the horizontal asymptote of this equation is 0.

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.

Assume the rational function is in its simplest form (if not, simplify it). If the denominator is a quadratic or of a higher power then it can have more than one roots and each one of these roots will result in a vertical asymptote. So, the graph of a rational function will have as many vertical asymptotes as there are distinct roots in its denominator.

2

Asymptotes

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.

Definition: If lim x->a^(+/-) f(x) = +/- Infinity, then we say x=a is a vertical asymptote. If lim x->+/- Infinity f(x) = a, then we say f(x) have a horizontal asymptote at a If l(x) is a linear function such that lim x->+/- Infinity f(x)-l(x) = 0, then we say l(x) is a slanted asymptote. As you might notice, there is no generic method of finding asymptotes. Rational functions are really nice, and the non-permissible values are likely vertical asymptotes. Horizontal asymptotes should be easiest to approach, simply take limit at +/- Infinity Vertical Asymptote just find non-permissible values, and take limits towards it to check Slanted, most likely is educated guesses. If you get f(x) = some infinite sum, there is no reason why we should be able to to find an asymptote of it with out simplify and comparison etc.

A sign chart helps you record data about a function's values around its _____ and _____ asymptotes. zeros vertical

Undefined; large

The answer depends on what you mean by "vertical of the function cosecant". cosec(90) = 1/sin(90) = 1/1 = 1, which is on the graph.