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

2 Answers
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

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]}