How do you determine if #f(x) = |x^2 + x|# is an even or odd function?

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Answer 1 · 2016-12-03T02:14:26

Neither.

#y>=0#.

#y(-x) is not y(x). So, it is not even. Y([x) is not -y(-x). So, it is not odd.

The given equation is the combined equation for the parabolas

#y=x^2+x, x>=0 and x<=-1# and

#y=-(x^2+x), x<=0 and x>=-1#.

As #y>-0#, the missing parts of the parabolas are not represented by

the given equation.

graph{y-|x^2+x|=0 [-5, 5, -2.5, 2.5]}