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Chapter 3: Problem 82

Use a graphing utility to graph the function. Be sure to use an appropriate viewing window. $$f(x)=\ln (x+2)$$

Short Answer

Expert verified
The graph of the function \(f(x)=\ln (x+2)\) shows a vertical asymptote at \(x = -2\) and a slow increase for \(x > -2\). Choose the viewing window as \(-2.5 < x < 10\) for the \(x\)-axis and \(-5 < y < 5\) for the \(y\)-axis.

Step by step solution

01

Identify the Function's Domain

The logarithmic function is only defined when \(x+2 > 0\), which means \(x > -2\). So the function's domain is \(-2 < x < \infty\). This will help us decide the viewing window for \(x\)-axis.
02

Choose an Appropriate Viewing Window

As for the vertical view, since this is the natural log function, it grows slowly. So a viewing window of around -5 to 5 is reasonable for the \(y\)-axis.
03

Graph the Function

Using the graphing utility of your choice, input the function \(f(x) = \ln (x+2)\) and set the viewing window. For \(x\), it should be slightly below -2 to a positive value of your choosing. For \(y\), it should be from -5 to 5. This will provide a good view of the overall graph.
04

Interpret the Graph

The graph displays the nature of the logarithmic function, showing a vertical asymptote at \(x = -2\) where the function is undefined, and the slow growth as \(x\) increases.

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