Calculus problems

ajone216 · #1 Oct 31, 2009, 08:54 AM

Graph the function f(x) = ex, state its domain and range, and give the equations of any
asymptotes. Do the same for g(x) = ln(x).

I have no idea how to get the equation of the asymptotes and I'm not perfect with domain and ranges. any help would be greatly appreciated.

Unknown008 · Oct 31, 2009, 09:22 AM

Have you ever seen the graphs of $y=e^x$ or $y = ln\ x$ ?

If not, try plotting them, and tell us what you got.

ajone216 · Oct 31, 2009, 05:36 PM

I can get the graph and I believe the domain is (-infiniti, infiniti) and the range is (0.infiniti)

Now I just need to find the equation of the asymptoes. My book doesn't show how to find the equations of asymptoes, just vertical and horizontal asymptoes. THANK YOU FOR YOUR HELP!!!

ajone216 · Oct 31, 2009, 05:38 PM

Sorry the domain should be (0, infiniti) and range (-infiniti, infiniti)

ajone216 · Oct 31, 2009, 06:33 PM

Can you tell me how to get the equations of asymptotes for e^x. and how to do it for other problems. that's the main thing I don't get. Thank you

Nhatkiem · Oct 31, 2009, 06:45 PM

Quote:

Originally Posted by ajone216

Can you tell me how to get the equations of asymptotes for e^x. and how to do it for other problems. that's the main thing I don't get. Thank you

the function e^x does indeed have asymptotes (remember asymptotes are a way of explaining end behaviors of graphs). Whenever you hear or see the word "end behavior" or "asymptote", you should be trying to visualize the graph as x tends to positive infinity, and as x tends to negative infinity.

Lightning55 · Oct 31, 2009, 07:20 PM

Quote:

Originally Posted by ajone216

Sorry the domain should be (0, infiniti) and range (-infiniti, infiniti)

Is it? As far as I know, e^x has a full open domain, however, the range must be positive. So your domain and range should be switched for e^x

ln(x) is pretty much the same. However, it's domain must be greater than zero because you can't have a negative natural log of something. And the log of something is always greater than zero right? What does that tell you about the range?

Unknown008 · Nov 1, 2009, 02:43 AM

Let's get it clear:

y = e^x has domain (-infinity, infinity) and range (0, infinity)
y = ln x has domain (0, infinity) and range (-infinity, infinity)

An asymptote is a line that your graph appears to be nearly touching and approaches it closer and closer, but never does. You'll notice for y = e^x that your graph appears to approach the x axis when it goes to -infinity, but actually never touches it. post your equations!



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