# Graphing e graphs

• August 6th 2011, 04:44 PM
sorkii
Graphing e graphs
Is there a faster way to graph expressions with 'e' in them? Whenever I graph them I have to put in a few x values manually into the expression to see what the graph looks like and then find the turning points

How do I find the asymptotes for these graphs? I'm having trouble with graphing y=x-e^x - Is the asymptote y=-1?

The other problem: one of the expressions is y=(e^x)/(x-1)
I've been taught that to find the asymptotes you divide everything by the highest x power in the denominator and anything when simplified is still over x is marked as a zero (something to do with limits)

What about (e^x)/x? Is it possible to simplify that?

Thanks!
• August 6th 2011, 05:53 PM
SammyS
Re: Graphing e graphs
I suppose you need to recognize that the graph $y=e^x$ only has a horizontal asymptote to the left, none to the right. That asymptote being the negative x-axis , i.e. y = 0 as x → -∞ .

The graph $y=e^{-x}$ is a reflection through the y-axis of $y=e^x\,.$

For the cases you mention, it's handy to be able to visualize the resulting graphs for adding/subtracting functions & multiplying/dividing functions.
• August 7th 2011, 02:09 AM
Siron
Re: Graphing e graphs
You're talking about asymptotes, but which asymptotes?
For example, if you have given: $f(x)=\frac{e^x}{x-1}$
H.A:
- $\lim_{x\to +\infty} \frac{e^x}{x-1}$, you can use in this case l'Hopitals rule and so you get:
$\lim_{x\to +\infty} e^{x}=+\infty$
- $\lim_{x \to -\infty}\frac{e^x}{x-1}=0$

So one H.A, $y=0$
...

Try to search for the other asymptotes.
You can't simplify $\frac{e^x}{x}$