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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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.
Think Domain of of y = e^x and Range of y = ln(x).
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).
It's a little colloquial, rather than technical, but I like it.
how would you explain it technically?
Fewer words and more symbols.