How do you graph #g(x)=abs(x^2-4)# using transformations?

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Answer 1 · 2016-12-10T02:29:32

See the graph and the explanation.

#y=|x^2-4| >=0# is the combined equation for the pair of parabolas

#y=X^2-4, x ouside [-2, 2] and#

#y=-(x^2-4), x in [-2, 2] .#

Note that Only the parts of the parabolas for #y>=0 are included.

Also, each is the mirror image of the missing part of the other, with

respect to the x-axis.

graph{y-|x^2-4|=0 [-10, 10, -5, 5]}