Expert: Scotto - 6/25/2009

Question
how to sketch graph of the function and how to determine the domain and range to this problem f(x)= square root of 9-x squared

Answer
First of all, the function is the function f(x) = √(9-x²)?

If it is, then |x| <= 3, for if |x| > 3, then x² > 9,
and we can't take the squareroot of a negative number.

To start on the graph,
just look at the 9 as a straight line from -3 to 3.

Once this is in your head,
then think about subtracting x² from that line.

What you have is a parabola opening downward.
When the square root is taken, it almost becomes a semicircle opening downward.

The domain is -3 to 3, for outside of there the function is undefined.  The range is from either endpoint, which is √(9-9) = 0 to the middle, which is √(9-0) = 3.

In Excel, you can put in an x range from -3 to 3 by 0.25 (or finer if you want) by putting -3 in the first cell and putting =(cell above)+0.25 in each cell below.  In the next column over,
put =sqrt(9-left cell^2).

If it you want it done easier than that, you should also use Excel.
You can highlight this, cut it with a cntl-X,
and paste it in Excel with a cntl-V.

-3   0
-2.75   1.198957881
-2.5   1.658312395
-2.25   1.984313483
-2   2.236067977
-1.75   2.436698586
-1.5   2.598076211
-1.25   2.727178029
-1   2.828427125
-0.75   2.90473751
-0.5   2.958039892
-0.25   2.989565186
0   3
0.25   2.989565186
0.5   2.958039892
0.75   2.90473751
1   2.828427125
1.25   2.727178029
1.5   2.598076211
1.75   2.436698586
2   2.236067977
2.25   1.984313483
2.5   1.658312395
2.75   1.198957881
3   0

Near the edges, it almost looks straight, but that is since I have a difference of 0.25 in the x values.  It would be smoother if the difference were smaller, but that would mean a lot more points.