We have the next function
[tex]f\mleft(x\mright)=\frac{x^2-e^x}{x}[/tex]We need to calculate the lim when x tends to -inf
[tex]\lim _{x\to-\infty}\frac{x^2-e^x}{x}=-\infty[/tex]Then we have that the left end behavior is
[tex]\: x\to\: -\infty\: ,\: f\mleft(x\mright)\to\: -\infty[/tex]