Answer
$\lim _{x\rightarrow \infty }\dfrac {3x^{2}-7}{x^{2}+5x}=3;\lim _{x\rightarrow -\infty }\dfrac {3x^{2}-7}{x^{2}+5x}=3;y=3$
Work Step by Step
$\lim _{x\rightarrow \infty }\dfrac {3x^{2}-7}{x^{2}+5x}=\dfrac {3-\dfrac {7}{x^{2}}}{1+\dfrac {5}{x}}=\dfrac {3-0}{1+0}=3$
$\lim _{x\rightarrow -\infty }\dfrac {3x^{2}-7}{x^{2}+5x}=\dfrac {3-\dfrac {7}{x^{2}}}{1+\dfrac {5}{x}}=\dfrac {3-0}{1+0}=3$
So the horizontal asymptote will be $y=3$
