Question

What is the domain and range of `y=absx -2`?

Answer 1

The domain is the set of real numbers R

For the range we note that

`y+2=|x|>=0=>y>=-2`

Hence the range is the set `[-2,+oo)`

Answer 2

Domain: `{x in RR}`
Range: `y = [-2,oo^+)`

Explanation:

The domain, in words is x is a real number, and the range is y
is greater than or equal to -2.

graph{|x|-2 [-10, 10, -5.21, 5.21]}

Absolute values are always positive numbers, since they express the distance a number is from zero, which seems pretty useless at first, but they are nice in instances such as chemistry, or physics, where you want to calculate percentage error.

`y=|x|-2` is like `y=x-2`, but all the `y` values must be greater than or equal to `-2`

Hope that helps!