In this activity Mr.Kelly gave us a photo of him shooting a basketball. First we made a prediction to see if we think the ball will make it in the hoop. I predicted that it will. We then had to use geogebra to figure if our prediction was accurate or not. By looking at this picture, the basketball has a chance of hitting the back of the backboard and going in or just completely bouncing out. It will not be a perfect swoosh. The graph shows the ball coming down into the hoop at a weird angle. It will most likely bounce at the very back of the hoop.
This function is a combination of three different kinds of graphs. In order to get a function for this graph you have to take all the functions of each graph and put them together. The functions for the line is y=-2x+2, the function for the half circle is y=+sqrt of 4-x^2, and the function for the puebla is y=(x-2)^2. The overall function for this graph is y= -2x+2 if x<0 sqrt of 4-x^2 if 0<x<2 (x-2)^2 if x>2.
For this activity, Mr. Kelly gave us the function y=x^2. We had to use desmos and draw the graph onto our plastic sheet. Next we had to find the inverse of y=x^2. We did that by making x=y^2. Then, we took the square root of both sides. Finally, x^2=+ or - the square root of x. We then graphed the function y=x took make our dotted line. We then folded the plastic sheet over the dotted line. The results of that is that the function y=x^2 is identical to the inverse function of that. In our example, our function did not have a inverse that was a function, but it is possible to have a function and its inverse be a function. FOr example, y=x. y=x is a function and its inverse is always a function. So, it is possible for a inverse to be a function.
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March 2015
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