Which quadrants and axes does #f(x)=abs(x)-6# pass through?

1 Answer
MeneerNask
Jun 9, 2016

It will pass all quadrants.
It will intersect the negative #y#-axis and both the positive and the negative #x#-axis.

Explanation:

Whatever value #x# has, #|x|# will never be negative.

But #f(x)=-6# if #x=0# (intersecting the #-y#-axis).
At #x=+-6# the value of #f(x)=0# (intersecting #+xand-x#-axis)

Axis-intersections are thus at #(-6,0),(0,-6),(+6,0)#
graph{|x|-6 [-16.02, 16.02, -8.01, 8.01]}

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