Recall that y = ln(x) and y = e^x are inverse functions. THe graph of y = ln(x) looks as though it might be approaching a horizontal asymptote. Write an argument based on the graph of y = e^x to explain why it does not.

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- October 2nd 2007, 07:57 PMMr_Greenln(x) and e^x
Recall that y = ln(x) and y = e^x are inverse functions. THe graph of y = ln(x) looks as though it might be approaching a horizontal asymptote. Write an argument based on the graph of y = e^x to explain why it does not.

- October 2nd 2007, 08:19 PMTKHunny
Think Domain of of y = e^x and Range of y = ln(x).

- October 2nd 2007, 08:22 PMMr_Green
does this make sense:

Since they are inverse functions, every (x,y) pair of ln(x) corresponds to a pair (y,x) of e^x. If ln(x) approaches a horizontal asymptote, that means that y has a limit. That means there is a limit on the x values of f(x). This is ridiculous, so obviously there is no horizontal asymptote for ln(x). - October 2nd 2007, 08:38 PMTKHunny
It's a little colloquial, rather than technical, but I like it.

- October 3rd 2007, 04:54 PMMr_Green
how would you explain it technically?

- October 3rd 2007, 08:20 PMTKHunny
Fewer words and more symbols.