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Chapter 1: Problem 38

Use a graphing utility to graph the function. Be sure to choose an appropriate viewing window. $$ k(x)=1 /(x-3) $$

Short Answer

Expert verified
The graph of the function \(k(x)=1/(x-3)\) with the viewing window centered around x=3, shows a vertical asymptote at x=3 with the function approaching negative infinity for x<3, and approaching positive infinity for x>3.

Step by step solution

01

Understand the Function

The function \(k(x) = 1/(x-3)\) is a rational function. It is undefined at x=3, indicating that the graph will have a vertical asymptote at x=3. Thus, the domain of this function is all real numbers except 3.
02

Choose the Viewing Window

An ideal viewing window for this function would be one that shows the behaviour of the function around the point x=3, where it is undefined. Hence, choose a range for x that centers around 3 and a range for y that will show the graph's broad behavior.
03

Graph the Function

Using the selected viewing window, plot the function \(k(x)=1/(x-3)\) in the graphing utility. The graph shows a vertical asymptote at x=3 and the function approaches to this asymptote from both sides, from negative infinity for x<3 and positive infinity for x>3. This is characteristic of the function \(k(x)=1/(x-a)\)

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