F (x)=|x-5|+|x+5|. Write f(x) as a piecewise function.?

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Answer 1 · 2018-04-18T12:30:07

Please see the explanation below

The function is

#f(x)=|x-5|+|x+5|#

#x-5>=0#, #=>#, #x>=5#

#x+5>=0#, #=>#, #x>=-5#

When #x<-5#

#f(x)=-x+5-x-5=-2x#

When #-5<=x<=5#

#f(x)=x+5-x+5=10#

When #x>5#

#f(x)=x-5+x+5=2x#

#f(x)={(-2x, "if " x <-5), (10, "if " -5<=x>=5), (2x, "if " x >5):}#

graph{|x-5|+|x+5| [-22.08, 23.52, 2.17, 24.98]}