how do you graph absolute value functions?

Question

Graph this absolute value function:

y= 3 l x-4 l - 2

how would i go about doing that?

Answer 1

You can see from the equation that it is linear
(a variant on y = ax + b)
so you will not have a curved result. But because of the absolute value term, you know there will be a point where the line will kink and head back up to the top (positive y) as x becomes smaller or more negative. Thus, the shape of the function is like the letter "V".
To find that point where the slope changes due to the absolute value term, look for where the absolute value expression goes negative. That is: for what x will x - 4 be zero or less?
You can see that x=4 will be the transition point because that is where the absolute value expression is zero.
You could do further algebra to determine the slope of the line on either side of x=4, but I'll assume for homework at your grade level this is not needed. (It would be nice for you to post your grade level in future questions.)
Knowing the shape of the function (V-shaped) you can plot the vertex (x=4) point and then one point to the left and one to the right of x=4, then connect the dots into a V shape, making the point of the "V" be at the x=4 position. To prove your graph is correct, calculate a few more (x,y) coordinates and make sure they fall on your V.

I think this is enough of a hint for you to make the graph yourself now.