what are the equations of the asymptotes of the graph of the function $f(x)=\frac{3x^{2}-2x - 1}{x^{2}+3x…

what are the equations of the asymptotes of the graph of the function $f(x)=\frac{3x^{2}-2x - 1}{x^{2}+3x - 10}$?\n$x=-5,x = 2$ and $y = 3$\n$x=-2,x = 5$ and $y = 3$\n$x = 3,y=-5$, and $y = 2$\n$x = 3,y=-2$, and $y = 5$

what are the equations of the asymptotes of the graph of the function $f(x)=\frac{3x^{2}-2x - 1}{x^{2}+3x - 10}$?\n$x=-5,x = 2$ and $y = 3$\n$x=-2,x = 5$ and $y = 3$\n$x = 3,y=-5$, and $y = 2$\n$x = 3,y=-2$, and $y = 5$

Answer

Explanation:

Step1: Find vertical asymptotes

Set the denominator equal to 0. Solve $x^{2}+3x - 10=0$. Factor: $(x + 5)(x - 2)=0$. So $x=-5$ or $x = 2$.

Step2: Find horizontal asymptote

Since the degrees of the numerator and denominator are the same (both degree 2), divide the leading - coefficients. The leading coefficient of the numerator is 3 and of the denominator is 1. So $y=\frac{3}{1}=3$.

Answer:

A. $x=-5,x = 2$ and $y = 3$