# How do you describe the transformation of #f(x)=-abs(x+4)+8# from a common function that occurs and sketch the graph?

##### 1 Answer

The graph of

#### Explanation:

The negative sign in front of the stuff connected to the x term means the graph flips over the x-axis. (It turns upside down because this is the equivalent of changing the sign of all the y values.)

Remember that whatever is added to or subtracted from the independent (x) variable moves the graph in the opposite direction.

Like, if you *add* three, the graph moves *left* three units, and if you *subtract* a number, the graph moves *right* that many units.

Finally, the eight tacked onto the end moves the graph vertically.

What I teach my students to do is put a finger over all the stuff connected to the

For sketching, definitely use the vertex you found at

The

If your teacher requires it, or you just feel like being a little more precise, it's easy to find your

(This makes sense because you're looking for the places where the function crosses the

If

Since the whole right-hand side is an absolute value expression, just use

So now you have the shape of the graph *and* all the intercepts to sketch with!