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New Member
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Oct 31, 2009, 08:54 AM
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Calculus problems
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.
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Uber Member
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Oct 31, 2009, 09:22 AM
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Have you ever seen the graphs of or ?
If not, try plotting them, and tell us what you got.
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New Member
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Oct 31, 2009, 05:36 PM
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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!!
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New Member
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Oct 31, 2009, 05:38 PM
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Sorry the domain should be (0, infiniti) and range (-infiniti, infiniti)
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New Member
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Oct 31, 2009, 06:33 PM
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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
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Junior Member
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Oct 31, 2009, 06:45 PM
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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.
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Junior Member
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Oct 31, 2009, 07:20 PM
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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?
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Uber Member
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Nov 1, 2009, 03:43 AM
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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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