Question

Write as a piecewise function. f(x) = abs(3x-2) + x

Answer 1

set 3x-2 equal to zero to find when the abs(x) affects the function then make that the domain of each of your peices

Answer 2

youll have to alter the part of the negative domain to retain the same co domain as the original function

Answer 3

so x = 2/3 right?

Answer 4

You can also refer to the definition of the absolute value function itself:
\[|x|=\begin{cases}x & \text{if $x\geq0$}\\
-x & \text{if $x<0$} \end{cases}\]
This means that
\[|3x-2|=\begin{cases}3x-2 & \text{if $3x-2\geq0$}\\
-(3x-2) & \text{if $3x-2<0$} \end{cases}\]