Algebra - Logarithm Functions

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Section 6.2 : Logarithm Functions

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21. Sketch the graph of \(g\left( x \right) = - \ln \left( x \right)\) .

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For this problem all we need to do is recall the Transformations section from a couple of chapters ago. Using the “base” function of \(f\left( x \right) = \ln \left( x \right)\) the function for this part can be written as,

\[g\left( x \right) = - \ln \left( x \right) = - f\left( x \right)\]

Therefore, the graph for this part is just the graph of \(f\left( x \right)\) reflected about the \(x\-axis.

The graph of this function is shown below. The blue dashed line is the “base” function, \(f\left( x \right)\), and the red solid line is the graph for this part, \(g\left( x \right)\).