How do you find the horizontal asymptote of f(x)=e^1/x?

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How do you find the horizontal asymptote of f(x)=e^1/x?

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Answer 1 · 2018-01-25T17:45:19

Please see below.

Explanation:

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Functions have horizontal asymptotes when the value of the function, i.e. the value of $f (x) = y$ $f(x)=y$ approaches a certain constant value as $x$ $x$ approaches $\infty$ $oo$ or $- \infty$ $-oo$ .

Let's plug $\infty$ $oo$ and $- \infty$ $-oo$ in for $x$ $x$ and see what happens:

$y = e^{\frac{1}{x}}$ $y=e^(1/x)$

$y = e^{\frac{1}{\infty}} = e^{0} = 1$ $y=e^(1/oo)=e^0=1$

$y = e^{\frac{1}{- \infty}} = e^{0} = 1$ $y=e^(1/-oo)=e^0=1$

This means $y = 1$ $y=1$ is a horizontal asymptote as can be seen in the graph of the function below:

![enter image source here]
( useruploads.socratic.org )

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How do you find the horizontal asymptote of f(x)=e^1/x?

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