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Chapter 1: Problem 61

Use a graphing utility to graph the equation. Use a standard setting. Approximate any intercepts. $$y=\frac{2 x}{x-1}$$

Short Answer

Expert verified
To approximate the intercepts, plot the function \(y=\frac{2 x}{x-1}\) using a graphing utility and examine where the function crosses the x and y axes. The nature of rational functions means that the graph may cross the axes at different points or not at all depending on the specific function.

Step by step solution

01

Identify the equation

The first step is to identify the given equation which in this case is \(y=\frac{2 x}{x-1}\). It's crucial to understand the nature of the equation which is a rational function, characterized by a ratio of two polynomial functions.
02

Graph the equation with a graphing utility

Given the rational function \(y=\frac{2 x}{x-1}\), input the expression into a graphing utility. Pay close attention to the range and domain to ensure you capture all significant points in the graph. Since the exercise does not specify a range or domain, use a standard setting which typically includes values reaching from -10 to 10 on both x and y axes.
03

Approximate the Intercepts

Once the graph of the function is plotted, the intercepts can be approximated. The x-intercept(s) is where the equation crosses the x-axis, that is where \(y = 0\). From the graph, determine where these points lie. Likewise, the y-intercept is where the equation crosses the y-axis, that is where \(x = 0\) which can be verified from the graph.

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