Today, Cress and Little (Mr. Kelly and his BFF) entertained us with a video of extreme sports, which was really them just shooting a basketball and trying to get it in the hoop and wearing crazy clothes. Our job was to find out if the ball was going to go into the hoop so we took the picture they provided for us of the ball at different heights on it's travel to the hoop, and inserted it into GeoGebra. I used the base of the ball to make the points, and then proceeded to put those points in a chart, made a list of the points, and then let GeoGebra do the math for me and come up with a function for me, it's depicted above but the function is f(x)=0.08x^2+1.29x+3.86. So, judging from the picture, and the line running into the backboard, I'm going to make an educated guess that the ball did not go into the hoop. Thanks to Cress and Little for coming up with these interesting activities for us and applying them to math! We really appreciate it! :)
The equation for this graph is y= -2x+2 is x< or equal to 0, square root of 4-x squared if 0 < or equal to 0 < or equal to 2, (x-2) squared is x > or equal to 2. This is called a piece wise function, hence the title piece wise functions.
This week's activity consisted of us learning about inverse's and their functions; how better to learn about that than actually physically doing it? Our math teacher, Mr. Kelly, had us graph the function x^2, and then find the inverse. The inverse is found by switching out the xs for the ys, for example, the function is y=x^2 therefore the formula becomes x=y^2. Now, to get y by itself, square rooting the x and y to get rid of the squared is necessary. When a variable is square rooted, it has to be + or - so the formula is now, + or - square root of x = y, then we graphed both of those functions, the + or -. It looked like the same function sideways, then we had to draw the y=x which is a diagonal line with a slope of 1 that passes through the origin. Folding our graph along that line, our two graphs should have lined up, however my dotted line sucked and it didn't line up remotely, but if I had drew it right, it would have. This is how to graph the inverse of a function. The function that we drew, x^2 passes the vertical line test, making it a function, but since the inverse does not pass the vertical line test, it is not a function. However there are functions that pass both, for example, y=x or practically any straight line, they pass the vertical and horizontal line test. Big thanks to our teacher for being creative and for being great at what he does!
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AuthorMy name is Evelyn Bradley and I'm in pre calculus! Archives
April 2015
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