Question

write the equation of the horizontal asymptote of the function: $y = \frac{x^{2}+x - 2}{-3x^{2}-5x + 3}$

Explanation:

Step1: Check degrees of polynomials

The degree of the numerator $x^{2}+x - 2$ is $n = 2$, and the degree of the denominator $-3x^{2}-5x + 3$ is $m=2$.

Step2: Find the horizontal - asymptote formula

When $n = m$, the horizontal asymptote is given by $y=\frac{a_{n}}{b_{m}}$, where $a_{n}$ is the leading coefficient of the numerator and $b_{m}$ is the leading coefficient of the denominator. Here, $a_{n}=1$ and $b_{m}=-3$.

Step3: Calculate the value of the horizontal - asymptote

$y=\frac{1}{-3}=-\frac{1}{3}$

Answer:

$y =-\frac{1}{3}$