Question

How do you write `y= abs (2x - 4)` as a piecewise function?

Answer 1

Use the definition of the absolute value function:

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

Explanation:

Given: `y= abs (2x - 4)`

Substitute the definition with `A = 2x-4`:

#y ={ (2x-4; 2x-4>=0), (-(2x-4); 2x-4<0) :}#

Simplify the inequalities:

#y ={ (2x-4; 2x>=4), (-(2x-4); 2x<4) :}#

#y ={ (2x-4; x>=2), (-(2x-4); x<2) :}#

Distribute the minus sign in the negative case:

#y ={ (2x-4; x>=2), (4-2x; x<2) :}" "larr# This is the answer.