Question

f(x)=e^(1/x)...i need help explaining the graph and how the exponent affects the graph's different portions so when x<0, 00.

Answer 1

did you graph it?

Answer 2

for big values of x \[\frac{1}{x}\] is small (closet to zero)
\[e^{\frac{1}{x}}\]gets close to
\[e^0=1\]

Answer 3

likewise as
\[x\rightarrow -\infty\]
\[\frac{1}{x}\rightarrow 0\] and so again you get 1, meaning you have a horizontal asymptote at y = 1

Answer 4

not defined at 0, but for small (close to zero) values of x,
\[\frac{1}{x}\] gets large and therefore
\[e^{\frac{1}{x}}\] gets really large

Answer 5

you can see the nice picture here
http://www.wolframalpha.com/input/?i=y%3De^%281%2Fx%29

Answer 6

i guess i should add that if x ->0 from the left you get large large negative numbers, so
\[lim_{x\rightarrow0^-}e^{\frac{1}{x}}=0\]