Graph y = 5x and y = log5x on a sheet of paper using the same set of axes. Use the graph to describe the domain and range of each function. Then identify the y-intercept of each function and any asymptotes of each function. (4 points)
Help? Explanation too please.
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I meant 5^x
Just enter a few x-values (something like -2, -1, 0, 1, 2) and find the corresponding y-value and sketch the graph. It should look like the attachment.
Domain is all the valid x-values, range is all the valid y-values.
logx is only defined for x>0, so it's domain is x>0. It's range is all real y-values. It has a vertical asymptote at x=0.
5^x has a domain of all real x-values, but it's range is limited to y>0. It has a horizontal asymptote at y=0.
It will come in handy to remember this:
Exponential functions (like 5^x) will have a *domain* of all real x-values.
Logarithmic functions (like log5x) will have a *range* of all real y-values.
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I did what you said and then graphed the inverse of the first function. Thank you and that tip was very helpful.
You're welcome :)
If you're allowed to bring notes into your test, that's a good one to have on there. Just something short, like:
Exponential functions - domain: all real x.
Logarithmic functions - range: all real y.