Question

question #10
true or false. if the horizontal asymptote of a rational function is y = -\frac{2}{3}, then the degree of the numerator will be less than the degree of the denominator.
false
true

Explanation:

Step1: Recall horizontal - asymptote rules

For a rational function $f(x)=\frac{P(x)}{Q(x)}$, where $P(x)$ is the numerator and $Q(x)$ is the denominator. If the degree of $P(x)$ is less than the degree of $Q(x)$, the horizontal asymptote is $y = 0$. If the degree of $P(x)$ equals the degree of $Q(x)$, the horizontal asymptote is $y=\frac{a}{b}$, where $a$ is the leading - coefficient of $P(x)$ and $b$ is the leading - coefficient of $Q(x)$. If the degree of $P(x)$ is greater than the degree of $Q(x)$, there is no horizontal asymptote.

Step2: Analyze given asymptote

The given horizontal asymptote is $y =-\frac{2}{3}$. This implies that the degree of the numerator and the denominator are equal.

Answer:

False