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

1 Answer
Vinícius Ferraz
Jul 7, 2015

Draw #P = (3,4)# and the semi-lines
#PA = (x, 6x - 14), x < 3#
and #PB = (x, 22- 6x), x > 3#

Explanation:

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

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

#f(3) = 4# This is a supremum vertex.

#x > 3 \Rightarrow f(x) = -6x + 18 + 4 = -6x + 22#

#x < 3 \Rightarrow f(x) = 6x - 18 + 4 =6x - 14#

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