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Chapter 3: Problem 69

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 function \(f(x) = \ln(x - 1)\) is only defined for \(x > 1\) with the range being all real numbers. The graph starts from the point (1,0) and increases slowly as x increases. Make sure to use an appropriate viewing window such as [1, 10] for the x-axis and [-5, 5] for the y-axis.

Step by step solution

01

Understanding the function

The first step is to understand the function \(f(x) = \ln (x - 1)\). The natural logarithm of x-1 is only defined for \(x > 1\). Thus, the domain of the function is \(x > 1\). The range of the function is all real numbers, \(-\infty < y < \infty\).
02

Choosing the Viewing Window

The next step is to choose an appropriate viewing window to graph the function. Since the function is only defined for \(x > 1\), one can start with the x-values from 1. To capture the full range of the function, it's suggested to choose y-values from \(-\infty\) to \(\infty\). However, since the function grows slowly, a reasonable window might be \(y \in [-5, 5]\). So, let's use a viewing window of [1, 10] for the x-axis and [-5, 5] for the y-axis.
03

Graphing the Function

Finally, one can graph the function using the chosen viewing window in a graphing utility. The graph starts from point (1,0), as natural logarithm of 0 equals 0. As x increases, y grows slowly and without bound. As a result, the function's graph will be increasing slowly, but steadily.

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