How do you graph g(x) in terms of f(x) for absolute function?

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SUMMARY

The discussion focuses on graphing the functions g(x) = f(|x|) and g(x) = |f(x)|, specifically in the context of the Spivak textbook, Chapter 4. It is established that g(x) will not necessarily take on a 'V' shape unless f(x) is a linear function of the form f(x) = kx + b. For g(x) = |f(x)|, the graph reflects the negative portions of f(x) around the x-axis, while positive intervals remain unchanged. An example provided is f(x) = x² - 1, where g(x) = |x² - 1| reflects the negative interval between -1 and 1.

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The graph of g is interm of f. So how to plot g(x)= f(|x|) and of g(x)=|f(x)|. Is it jus a 'V' shape one.This problem is in Spivak Textbook, Chapter 4. Thanks to all.:confused:
 
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Well, it won't be a V function, unless f(x) is a linear function, that is of the form f(x)=kx+b. However, the expression g(x)=|f(x)| means that your g function will be graphed in that manner that in whatever interval f(x) is positive, g(x) will remain unchanged, however, in whatever interval f(x) is negative, your g(x) will be reflected around the x-axis. Say for example that f(x)=x^2-1. then this function is negative from -1 to 1. so this portion of the graph will be reflected around x-axis while the other part will remain unchanged if g(x)=|f(x)|=|x^2-1|
 

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