Determine the piecewise representation of​ f(x) below:

Question

|3x-6|

Equation A if x>=a

Equation B if x<b

I do not understand how to create the formulas

i did

3x-6=0

x=2

and i believe the domain of a would be (-infinity, 2)

and domain of b would be (2, infinity)

I followed another tutorial on how to do it and i know

equation A = 3x-6

and B= -3x+6

but i dont know why!

Answer 1

Use the definition of absolute value:

|A| = A if A ≥ 0

|A| = -A if A < 0

In your example "A" is equal to 3x - 6. So the first step is to find where 3x - 6 ≥ 0 (this is when x ≥ 2) and where 3x - 6 < 0 (this is when x < 2).

So f(x) = 3x - 6 when x ≥ 2.

When x < 2, then 3x - 6 < 0, so f(x) is equal to -(3x - 6) = -3x + 6.