What is the graph of the absolute value function #y = 3 - abs(x - 3)#?

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Answer 1 · 2017-07-01T16:09:30

See below

Let's look at this problem like this. The graph of #y=abs(x)# looks like this:

graph{abs(x) [-10, 10, -5, 5]}

Now let's see what thee #-3# does. The graph of #y=abs(x-3)# looks like this:

graph{abs(x-3) [-10, 10, -5, 5]}

As you can see, it shifted the entire graph #3# units to the right.

`Finally, let see what the #3# outside the absolute value sign does:

graph{3-abs(x-3) [-10, 10, -5, 5]}

Basically, the #-# sign caused the graph to be flipped around the x-axis and the #3# shifted the graph up #3# units.

If the function was #y=3+abs(x-3)# the graph will NOT be flipped. It will just be shifted #3# units to the right and #3# units up.