Mathematics

Problem

The exponential function

y=e^{x}

and the logarithmic function

y=\ln x

are to be drawn on the same set of axes. a. (i) For each function, find its domain, range and intercept(s) with the coordinate axes. b. (ii) Locate any vertical asymptote(s) and describe the end behaviour of each function as

x\to\infty

. c. (iii) Using the information obtained, sketch the graphs of

y=e^{x}

and

y=\ln x

together for

0< x\le 4

. Clearly label the asymptote, intercepts and indicate how the two curves behave relative to each other.

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