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Why do Rational functions have asymptotes?

Answer 1

Nathan Axel

Because they cannot ever touch those zones, and they never will.

Refer to this function:

#f(x)=1/x#

It should look something like this:

Basically, asymptotes are hypothetical positions a function may approach, but will never touch.

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Answer 2

Nathan Axel

Rational functions have asymptotes because they are defined as the ratio of two polynomial functions. Asymptotes occur when the denominator of the rational function becomes zero, resulting in an undefined value. These values are important because they indicate the behavior of the function as it approaches certain points or values. Horizontal asymptotes occur when the degree of the numerator is less than or equal to the degree of the denominator, while vertical asymptotes occur when the denominator becomes zero at certain values.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.