SOLUTION: Can anyone help me with this? I just need to sketch the graph of the following function, but need to also know how it's done. f(x) = 3- In x The answer shows it as intersec

Question 22299: Can anyone help me with this?
I just need to sketch the graph of the following function, but need to also
know how it's done.
f(x) = 3- In x
The answer shows it as intersecting the x axis at (20,0)
Domain x>0
V. axymptote = x axis x = 0
Can anyone help?
Thanks
Sandy
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
I can't sketch it for you here but can describe how you should do that.
Hopefully you know what the graph of lnx looks like. It has x=0 as an
asymptote, passes upward through (1,0) and gradually rises as x gets larger
and larger.
Now your equation has a negative sign before lnx. That flips the lnx
graph over on the x-axis. It still passes through (1,0) and still has
x=0 as an asymptote, but now it gets more and more negative as x gets
larger and larger.
The "3" in your equation raises every point in the graph upward by "3".
So now it doesn't pass through (1,0); instead it passes through (1,3),
and yes, it passes through (20.086,0).
Cheers,
Stan H.

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