How do you write #H(x) = 2/3|x-5|# as piecewise functions?

1 Answer
Aug 13, 2017

Answer:

Use the definition of the absolute value function:

#|A| = {(A; A >=0),(-A; A < 0):}#

Explanation:

Given: #H(x) = 2/3|x-5|#

Use the definition:

#H(x) = 2/3{(x-5; x-5 >=0),(-(x-5); x-5 < 0):}#

Simplify the domain restrictions:

#H(x) = 2/3{(x-5; x >=5),(-(x-5); x < 5):}#

Distribute the minus sign:

#H(x) = 2/3{(x-5; x >=5),(-x+5; x < 5):}#

Distribute the #2/3#:

#H(x) = {(2/3x-10/3; x >=5),(-2/3x+10/3; x < 5):}#