Exponentially True Or Exponentially False

As $x\to-\infty$ $e^x\to 0$ so the graph of the function has a horizontal asymptote. Suppose that such reflection line existed. Then $e^x$ should have a sloped asymptote as $x\to\infty$ . For a sloped asymptote $y=ax+b$ to exist for a function $f(x)$ , it should satisfy $\lim_{x\to\infty}\frac{f(x)}{x}=a$ Here $a$ must be a finite value. It's simple to prove that this doesn't hold for $f(x)=e^x$ so no sloped asymptote exists, thus a contradiction. So the statement is False.