Question

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

Answer 1

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

Answer 2

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]}