Question

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

Answer 1

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]}