Write $f ( x ) = 5 + | 3 x - 2 |$ as a piecewise function.
A) $f ( x ) = \left\{ \begin{array} { c c }
- 3 + 3 x & x

Question

Write $f ( x ) = 5 + | 3 x - 2 |$ as a piecewise function.
A) $f ( x ) = \left\{ \begin{array} { c c } 
- 3 + 3 x & x < 2 / 3 \
3 - 3 x & x \geq 3 / 2
\end{array} \right.$
B) $f ( x ) = \left\{ \begin{array} { c c } 
- 3 - 3 x & x < 2 / 3 \
3 + 3 x & x \geq 2 / 3
\end{array} \right.$
C) $f ( x ) = \left\{ \begin{array} { l l } 
7 - 3 x & x < 2 / 3 \
3 + 3 x & x \geq 2 / 3
\end{array} \right.$
D) $f ( x ) = \left\{ \begin{array} { l l } 
7 + 3 x & x < 2 / 3 \
3 - 3 x & x \geq 2 / 3
\end{array} \right.$

Quizplus · Accepted Answer

The absolute value function $|3x - 2|$ splits into two cases: $3x - 2$ when $3x - 2 \geq 0$ (or $x \geq 2/3$) and $-(3x - 2)$ when $3x - 2 < 0$ (or $x < 2/3$). For $x < 2/3$, the function is $5 - (3x - 2) = 7 - 3x$. For $x \geq 2/3$, it is $5 + (3x - 2) = 3 + 3x$.

Write f(x)=5+∣3x−2∣f ( x ) = 5 + | 3 x - 2 |f(x)=5+∣3x−2∣

Write $f ( x ) = 5 + | 3 x - 2 |$