Is #y=|x|# a linear function?

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Answer 1 · 2018-02-27T22:11:10

No.

An interesting fact:

A function is linear if:

#f(ax+y)=af(x)+f(y)#

Now, we have:

#f(x)=absx#

Let's try

#a=1#

#x=2#

#y=-3#

#=>f(ax+y)?af(x)+f(y)#

#=>abs(ax+y)?aabsx+absy#

#=>abs(1*2+(-3))?1*abs2+abs(-3)#

#=>abs0?2+3#

#=>0!=5#

Therefore, our function is not linear.