How do you write #y=abs(x+2)# as a piecewise function?

1 Answer
Jun 1, 2017

Answer:

#y = -x -2; " " x < -2#
#y = x + 2; " " x >= -2#

Explanation:

Given: #y = |x + 2|#

An absolute function always has two pieces. #y = |f(x)|# can always be broken into two pieces:

#y = -(f(x)); " " x < f(x) = 0#
# y = +(f(x)); " " x >= f(x) = 0#

With the given function, #f(x) = x + 2#

Find where #f(x) = 0: " "x + 2 = 0; " " x = -2#

Two pieces of the function become:

#y = -(x + 2) = -x - 2; " " x < -2#

#y = +(x + 2) = x + 2; " " x >= -2#