annie1799
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Decide whether the following statement is true or false. If the degree of the numerator of a rational function equals the degree of the​ denominator, then the rational function has a horizontal asymptote. Choose the correct answer below.
A. The statement is true because if the degree of the numerator of a rational function equals the degree of the​ denominator, then the rational function has a horizontal asymptote that is equal to the product of the leading coefficients.

B. The statement is true because if the degree of the numerator of a rational function equals the degree of the​ denominator, then the rational function has a horizontal asymptote that is equal to the ratio of the leading coefficients.

C. The statement is false because if the degree of the numerator of a rational function equals the degree of the​ denominator, then the rational function has no horizontal or oblique asymptotes.

D. The statement is false because if the degree of the numerator of a rational function equals the degree of the​ denominator, then the rational function has an oblique asymptote that is equal to the quotient found using polynomial division.

Respuesta :

B. The statement is true because if the degree of the numerator of a rational function equals the degree of the​ denominator, then the rational function has a horizontal asymptote that is equal to the ratio of the leading coefficients.

This is about understanding conditions to have horizontal asymptotes.

Option B is correct.

  • A graph of a rational function is said to have horizontal asymptote if it approaches the horizontal line as the value of x keeps increasing.

For a function to be a horizontal asymptote, it must fall into one of these 3 categories.

  • If the degree of the numerator of the rational function is less than the degree of the denominator, then we can say that the horizontal asymptote of that function is always the x axis.

  • If the degree of the numerator and denominator of the rational function are equal, then the horizontal asymptote will always be the ratio of the leading coefficients.  

  • If we have a case whereby the degree of the numerator is greater than that of the denominator, then it means there cannot be a  horizontal asymptote because it implies that the y-values are increasing without boundary as x is increasing in magnitude.

Looking at the given options, the only one that falls into the conditions for horizontal asymptote as stated above is option B which tallies with the second condition i gave above.

Read more at; https://brainly.com/question/21693166

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