Home > Algebra > Graphs in the Coordinate Plane

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

Answer 1

Avery Alexander

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

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]}

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Abigail Allen

The function f(x) = |x| - 6 passes through quadrants I and IV and intersects the x-axis at x = ±6.

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 3

Eva Adamson

The function f(x) = |x| - 6 passes through Quadrants I and IV and intersects both the x-axis and the y-axis.

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.