How do you simplify #abs(33)#?

1 Answer
Aug 3, 2015

#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.