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Chapter 1: Problem 68

Use a graphing utility to graph the equation. Use a standard setting. Approximate any intercepts. $$y=2-|x|$$

Short Answer

Expert verified
The graph of the function \(y = 2 - |x|\) is a 'V' shaped graph with its lowest point at (0,2). It has y-intercept at (0,2) and x-intercepts at (-2,0) and (2,0).

Step by step solution

01

Understand the function

We need to graph the function \(y = 2 - |x|\). This is a linear absolute function, meaning that its graph should have a V shape. The value inside the absolute function |x| can take any real number and its output will always be non-negative. The negative sign and +2 outside the absolute function will vertically shift the graph down and up respectively.
02

Set up the graph

Set up a graph with an x and y-axis. The standard setting means that both axes should range at least from -10 to 10, in order to accommodate all common real values.
03

Graph the function

Starting the line at the point (0,2), the graph will slope downwards to the right and left because of the negative in front of the absolute function. The graph should make a 'V' shape, with the bottom of the V at the point (0,2).
04

Approximate the intercepts

Intercepts are points where the graph crosses the x or y axes. In this case, we can see that the intercepts occur at (0,2) for the y-intercept, and (2,0) and (-2,0) for the x-intercepts.

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