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