Question

How do you simplify `abs(33)`?

Answer 1

`abs(33) = 33`

Explanation:

The absolute value function is a special class of function called a piecewise function. What this means is it has more than one definition that depends on the input.

Those definitions are:
if `x>=0` then `abs(x) = x`
if `x<0` then `abs(x) = -x`

so for our example `33>=0` so
`abs(33) = 33`

The above is the technical definition of the function. However, I think it is easier to think about it as a distance function. The absolute value tell you how far a number is from zero. Then it becomes obvious what the value should be.

`abs(5) = 5` because +5 is 5 away from zero
`abs(-5) = 5` because -5 is 5 away from zero

and this is simplification makes us happy.