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Chapter 1: Problem 25

Use a graphing utility to graph the function. Be sure to choose an appropriate viewing window. $$g(x)=|x|-5$$

Short Answer

Expert verified
The graph is a V-shaped curve, opening upwards, originating from the point (0, -5). It has been shifted down by 5 units compared to the parent function \(g(x)=|x|\). The viewing window should range -10 to 10 on the x-axis and -10 to 5 on the y-axis to appropriately illustrate the graph.

Step by step solution

01

Understand the Function

Recognize that we're working with an absolute function. It will help us understand that an absolute function graph opens upwards if the coefficient of |x| is positive, and opens downwards if the coefficient is negative. The graph of \(g(x)=|x|\) is a V-shaped graph. The transformation -5 will shift that graph down by 5 units. Thus, the vertex of the new graph will be (0, -5).
02

Choose an Appropriate Viewing Window

Select a window that adequately displays the critical features of the function. A suitable viewing window could be -10 to 10 on the x-axis (to showcase the V-shape), and -10 to 5 on the y-axis (to encompass the -5 shift).
03

Plot the Function and Apply the Transformation

Enter the function \(g(x)=|x|-5\) in the graphing utility. Apply the -5 transformation to shift the graph downwards. Plot points to understand the shape, ensuring the graph shows the V-shape appropriately.

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