# How do you graph  f(x) = -2abs(3x-9)+ 4?

Jul 7, 2015

Draw $P = \left(3 , 4\right)$ and the semi-lines
$P A = \left(x , 6 x - 14\right) , x < 3$
and $P B = \left(x , 22 - 6 x\right) , x > 3$

#### Explanation:

$| 3 x - 9 | = 3 x - 9$, if $3 x - 9 \setminus \ge 0 \setminus \Leftrightarrow 3 x \setminus \ge 9 \setminus \Leftrightarrow x \setminus \ge 3$

$| 3 x - 9 | = - 3 x + 9$, if $3 x - 9 < 0 \setminus \Leftrightarrow 3 x < 9 \setminus \Leftrightarrow x < 3$

$f \left(3\right) = 4$ This is a supremum vertex.

$x > 3 \setminus R i g h t a r r o w f \left(x\right) = - 6 x + 18 + 4 = - 6 x + 22$

$x < 3 \setminus R i g h t a r r o w f \left(x\right) = 6 x - 18 + 4 = 6 x - 14$