find the horizontal asymptote(s), if any, of the graph of the rational function. f(x) = (-5x - 3)/(3x + 4)…

find the horizontal asymptote(s), if any, of the graph of the rational function. f(x) = (-5x - 3)/(3x + 4) oa. y = -3/4 ob. y = -5 oc. y = -5/3 od. no horizontal asymptote

find the horizontal asymptote(s), if any, of the graph of the rational function. f(x) = (-5x - 3)/(3x + 4) oa. y = -3/4 ob. y = -5 oc. y = -5/3 od. no horizontal asymptote

Answer

Explanation:

Step1: Identify degrees of polynomials

The degree of the numerator $-5x - 3$ is 1 and the degree of the denominator $3x+4$ is 1.

Step2: Use horizontal - asymptote rule

For a rational function $\frac{f(x)}{g(x)}$ where $\text{deg}(f)=\text{deg}(g)=n$, the horizontal asymptote is $y = \frac{a_n}{b_n}$, where $a_n$ and $b_n$ are the leading coefficients of $f(x)$ and $g(x)$ respectively. Here, $a_n=-5$ and $b_n = 3$. So the horizontal asymptote is $y=-\frac{5}{3}$.

Answer:

C. $y =-\frac{5}{3}$