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Chapter 4: Problem 130

Graph \(f\) and \(g\) in the same viewing rectangle. Then describe the relationship of the graph of g to the graph of \(f\). $$f(x)=\log x, g(x)=-\log x$$

Short Answer

Expert verified
The graph of \(g(x)=-\log x\) is the reflection of the graph of \(f(x)=\log x\) over the x-axis.

Step by step solution

01

Sketch the graph of \(f(x)=\log x\)

Begin by sketching the graph of \(f(x)=\log x\). The graph of \(f(x)=\log x\) is a smooth curve that crosses the x-axis at x=1 and then increases without bound to the right while it moves closer to the x-axis but never touches or crosses it, as \(x\) moves to the left.
02

Sketch the graph of \(g(x)=-\log x\)

The graph of \(g(x)=-\log x\) can be obtained from the graph of \(f(x)=\log x\) by reflecting the latter in the x-axis. This is because the negative sign only affects the y-coordinates of the points on \(f\), leaving the x-coordinates unchanged.
03

Compare the graphs

After sketching the graphs of both functions, compare them. You will notice that the graph of \(g(x)=-\log x\) is simply the reflection of the graph of \(f(x)=\log x\) over the x-axis.

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