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

2 Answers
Dharma R.
Sep 21, 2015

Explanation:

graph{-3|x+2|+2 [-11.24, 11.26, -5.625, 5.63]}
f(x)=-3|x-2|+2=0
|x-2|=2/3
=>x-2=2/3, -(x-2)=2/3
x=8/3r x=4/3

İnci
Sep 21, 2015

You can graph it step by step.

Explanation:

Firstly, let's graph the absolute term #|x + 2|#

When we give values to #x#
#x = -2#
#|x + 2| = 0#

#x=0#
#|x+2|=2#

#x=-1#
#|x+2|=1#

#x=1#
#|x+2|=3#

#x=-3#
#|x+2|=1#

graph{|x + 2| [-4.093, 0.907, -0.41, 2.09]}

You can see that #y# is always positive and the slope of right part of graph is #1#
Then, we must consider the coefficient of #|x+2|# . The coefficient #(-3)# is going to make the graph narrower and upside down because of negative value. The slope is going to be #(-3)#
graph{-3|x+2| [-4.175, 0.825, -2.42, 0.08]}

The final part is adding the last term of function. The term #2# is going to locate the graph #2# units upper on ordinate.

#x=0#
#-3|x+2| =-6#

#x=0#
#-3|x+2|+2=-4#

Finally, we have:
graph{-3|x+2|+2 [-6.893, 3.107, -2.49, 2.51]}

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