AboutScotto Expertise Any kind of mathematics (calculus, analysis, game theory, linear approximation, finite differences, linear regression, linear programming, numerical analysis, probability, statistics, etc.).
I also have answered some questions in
Physics (mass, momentum, falling bodies),
Chemistry (charge, reactions, symbols, molecules), and
Biology.
Experience Experience in the area: I have tutored students in all areas of mathematics for over 20 years.
Education/Credentials: BSand MS in Mathematics from Oregon State University, where I completed sophomore course in Physics and Chemistry. I received both degrees with high honors.
Awards and Honors: I have passed Actuarial tests 100, 110, and 135.
Publications Maybe not a publication, but I have respond to well oveer 3000 questions on the PC.
That's around 2,000 in basic math and 1,000 in advanced math.
Education/Credentials I aquired well over 40 hours of upper division courses. This was well over the number that were required.
I graduated with honors in both my BS and MS degree from Oregon State University.
I was allowed to jump into a few junior level courses my sophomore year.
Awards and Honors I have been nominated as the expert of the month several times.
All of my scores right now are at least a 9.8 average (out of 10).
Past/Present Clients My past clients have been students at OSU, students at the college in South Seattle,
referals from a company, friends and aquantenances, people from my church, and people like you.
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.
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.
