Answer
$\lim _{x\rightarrow \infty }\dfrac {x^{4}+7}{x^{5}+x^{2}-x}=0;\lim _{x\rightarrow -\infty }\dfrac {x^{4}+7}{x^{5}+x^{2}-x}=0;y=0$
Work Step by Step
$\lim _{x\rightarrow \infty }\dfrac {x^{4}+7}{x^{5}+x^{2}-x}=\dfrac {\dfrac {1}{x}+\dfrac {7}{x^{5}}}{1+\dfrac {1}{x^{3}}-\dfrac {1}{x^{4}}}=\dfrac {0+0}{1+0-0}=\dfrac {0}{1}=0$
$\lim _{x\rightarrow -\infty }\dfrac {x^{4}+7}{x^{5}+x^{2}-x}=\dfrac {\dfrac {1}{x}+\dfrac {7}{x^{5}}}{1+\dfrac {1}{x^{3}}-\dfrac {1}{x^{4}}}=\dfrac {0+0}{1+0-0}=\dfrac {0}{1}=0$
so the horizontal asymptote will be $y=0$
