You can
put this solution on YOUR website!Let's write |x| as a function:
f(x) = |x|
Let's solve for f(x) when x > 0. We know that for all x > 0, the absolute value doesn't change anything, since x is already positive. Therefore:
For x > 0, f(x) = x
We also know that for all x < 0, the absolute value makes the negative number positive again. Multiplying the negative number x with -1 has the same effect, so:
For x < 0, f(x) = -x
Now we need to know f(x) when x = 0.
f(x) = |0| = 0
The number didn't change. Therefore:
For x = 0, f(x) = x
Combining everything together:
The piecewise function of f(x) = |x| is
for x >= 0, f(x) = x
for x < 0, f(x) = -x
