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

Jul 1, 2017

See below

Explanation:

Let's look at this problem like this. The graph of $y = \left\mid x \right\mid$ looks like this:

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

Now let's see what thee $- 3$ does. The graph of $y = \left\mid x - 3 \right\mid$ 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 $y = 3 + \left\mid x - 3 \right\mid$ the graph will NOT be flipped. It will just be shifted $3$ units to the right and $3$ units up.