Q: Why are asymptotes important characteristics of rational functions?

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Nope not all the rational functions have a horizontal asymptote

That's the definition of a "rational function". You simply divide a polynomial by another polynomial. The result is called a "rational function".

yes

false

A rational number can always be written as (one whole number) divided by (another whole number). That's not only a characteristic of a rational number, it's the definition of one.

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

No, it will always have one.

Because they are represented as fractions.

There are some characters missing from the question and, without them, the question makes no sense and so cannot be answered.

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.

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.

Yes. Rational functions must contain rational expressions in order to be rational.

Yes. Rational functions must contain rational expressions in order to be rational.

Yes. Rational functions must contain rational expressions in order to be rational.

Yes. Rational functions must contain rational expressions in order to be rational.

Rational values- those are necessary to the functions and fulfillment of intellect and will.

a