Question

For a rational function in the form f(x)= q(x)/p(x)what can be determined about the end behavior from the degrees of the numerator and denominator polynomials?

A) The end behavior is always increasing.

B) The end behavior is always decreasing.

C) The end behavior is determined by the degrees of the numerator and denominator.

D) The end behavior is independent of the degrees of the numerator and denominator.
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Answer 1

The end behavior of a rational function is determined by the degrees of the numerator and denominator polynomials.

Step-by-step explanation:

The end behavior of a rational function can be determined by the degrees of the numerator and denominator polynomials.

If the degree of the numerator is greater than the degree of the denominator, the end behavior will have a slant asymptote. If the degree of the numerator is equal to the degree of the denominator, the end behavior will have a horizontal asymptote. If the degree of the numerator is less than the degree of the denominator, the end behavior will approach 0 or infinity, depending on the leading term of the denominator.

Therefore, the correct answer is C) The end behavior is determined by the degrees of the numerator and denominator.