decide whether the following statement is true or false. if the degree of the numerator of a rational…

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 ratio of the leading coefficients gives rise to the horizontal asymptote. choose the correct answer below. true false

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 ratio of the leading coefficients gives rise to the horizontal asymptote. choose the correct answer below. true false

Answer

Explanation:

Step1: Recall rational - function asymptote rule

For a rational function $f(x)=\frac{a_nx^n + a_{n - 1}x^{n-1}+\cdots+a_0}{b_mx^m + b_{m - 1}x^{m-1}+\cdots+b_0}$, when $n = m$ (where $n$ is the degree of the numerator and $m$ is the degree of the denominator), $\lim_{x\rightarrow\pm\infty}f(x)=\frac{a_n}{b_m}$.

Step2: Identify horizontal asymptote

The line $y = \frac{a_n}{b_m}$ (the ratio of the leading - coefficients) is the horizontal asymptote of the rational function when the degree of the numerator equals the degree of the denominator.

Answer:

True