SOLUTION: f(x)=-2|-3x-6|+4 graph and find domain and range. This is the question on my quiz today. Im not sure that it was +4 but i think it was. can you please show table of values

Algebra ->  Systems-of-equations -> SOLUTION: f(x)=-2|-3x-6|+4 graph and find domain and range. This is the question on my quiz today. Im not sure that it was +4 but i think it was. can you please show table of values      Log On


   

Question 914236: f(x)=-2|-3x-6|+4
graph and find domain and range.
This is the question on my quiz today. Im not sure that it was +4 but i think it was.
can you please show table of values and the process, I was really lost.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
A table of values is just a way to begin learning how to pick points of functions and make a graph. You can pick values yourself for x and evaluate the corresponding f(x) for each.

More useful is to analyze the function and graph it from knowledge about the function.

There is a critical x value, -3x-6=0
x%2B2=0
x=-2 at which a corner occurs.

When -3x-6>=0,
f%28x%29=-2%28-3x-6%29%2B4
f%28x%29=6x%2B12%2B4
f%28x%29=6x%2B16
Corresponding to x%3C=-2.

When -3x-6<0,
f=-2%28-1%29%28-3x-6%29%2B4
f=2%28-3x-6%29%2B4
f=-6x-12%2B4
f=-6x-8
Corresponding to x%3E-2.

Each of those is a linear equation, but a corner occurs at x=-2.

graph%28300%2C300%2C-10%2C10%2C-10%2C10%2C-2%2Aabs%28-3x-6%29%2B4%29

If you really want to make a data table for x and y, start with x at -4, pick increasing integer values up until about +4....

____x____________y=f(x)=-2*abs(-3x-6)+4
___-4__________________-2abs(-3(-4)-6)+4
___-3__________________
___-2__________________fillin the rest...
___0
____1
____2