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Chapter 3: Problem 70

Use a graphing utility to graph the function. Be sure to use an appropriate viewing window. \(f(x)=\ln (x-1)\)

Short Answer

Expert verified
The graph of the function \(f(x)=\ln (x-1)\) shows the typical shape of a logarithmic function, only defined for values \(x>1\), and increasing slowly without limit.

Step by step solution

01

Initialize the Graphing Utility

First, you'd set up your graphing utility. There are many options available, such as graphing calculators, computer software, or online tools. Once you've chosen your tool, make sure you understand how to input functions, adjust the viewing window, and interpret the graph.
02

Input the Function

Next, you'd input the function. In this case, the function is \(f(x)=\ln (x-1)\). Make sure that the function is entered correctly to avoid any errors.
03

Choose the Viewing Window

Now, you'd need to select an appropriate viewing window. Since the function is only defined for \(x>1\), you would choose the x-values to be greater than 1. For the y-values, since this is a logarithmic function which can grow large as x gets bigger, you can start with a wider range, such as from -10 to 10, and adjust it as needed.
04

Display the Graph

Finally, use the graphing tool to display the graph. Make sure you look at the shape and behavior of the graph to understand the properties of the function. Adjust the y-range if necessary to see the entire function. The graph should show the typical shape of a logarithmic function, increasing slowly and without a limit, and undefined for values \(x \leq 1\).

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Most popular questions from this chapter

Solve the logarithmic equation algebraically. Approximate the result to three decimal places. $$6 \log _{3}(0.5 x)=11$$

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Use the acidity model given by \(\mathbf{p H}=-\log \left[\mathbf{H}^{+}\right],\) where acidity \((\mathbf{p H})\) is a measure of the hydrogen ion concentration \(\left[\mathbf{H}^{+}\right]\) (measured in moles of hydrogen per liter) of a solution. The \(\mathrm{pH}\) of a solution decreases by one unit. By what factor does the hydrogen ion concentration increase?
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