APFIVE Limits at Infinity and Horizontal Asymptotes
Which of the following correctly describes a function whose limit as $$x \to \infty$$ indicates a horizontal asymptote?
A
For the function $$p(x)=\frac{e^x}{x}$$, the exponential numerator causes the function to diverge to infinity, eliminating a horizontal asymptote.
B
For the function $$h(x)=e^{x}$$, the function grows without bound, so no horizontal asymptote exists.
C
For the function $$f(x)=e^{-x}$$, as $$x\to\infty$$ the value of the function approaches 0, revealing a horizontal asymptote at $$y=0$$.
D
For the function $$g(x)=x*e^{-x}$$, although the limit is 0, the role of the polynomial factor complicates the demonstration of a horizontal asymptote.
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