Question 459333: #5 on homework.
sketch graph of function f(x)=log2(x+1) by transforming y=log2x
Find domain and vertical asympote
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! sketch graph of function f(x)=log2(x+1) by transforming y=log2x
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I don't have the means to draw a graph for you, but I can show you how to do it.
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Start with the basic log function: y=logx
The first point on the graph to note is (1,0), that is, when x=1, y=0.
When x<1, approaching asymptote, y-axis or x=0, y becomes increasingly negative.
When x>1, y becomes increasingly positive but at a slower rate.
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y=log2x
This moves the (1,0) point to the (1/2,0) point.
The asymptote, x=0, does not change, but the point at which y goes from negative to positive is at x=1/2 instead at x=1 as in the basic function. Both curves have similar shapes with the log2x curve sitting above the logx curve
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log2(x+1)
This just moves previous curve one unit to the left, placing the asymptote at x=-1 instead of x=0, and moving the (1/2,0) point to the (-1/2,0) point. Curve also sits above previous curve.
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Hope this helps you understand the log curves.
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