How to Express f(x)=lxl as a piecewise function?

Question

Can you please show me the steps on how to express this into a piecewise function? I don't understand it at all.

Answer 1

f(x) = -x       when  x ≤ 0

f(x) = x        when  x ≥ 0

 

The two pieces share a common point at x=0.  That point is (0, 0).

Answer 2

If x < 0, then l x l = -x  For example, l -2 l = 2 = -(-2)

 

If x ≥ 0, then l x l = x   For example, l 5 l = 5

 

 

          -x, if x < 0

f(x) = 

           x, if x ≥ 0

 

 

Answer 3

             /

            |   x  if x ≥ 0

f(x) = <

            |  -x  if x < 0

             \

 

Examples:

• If x = 2, then f(x) = x = 2
• If x = -2, then f(x) = -(-2) = 2