This is my master piece for families of functions! I used the online calculator known as demos.com to enter in random functions and see the outcome. I had no idea what I was doing at first. to be honest i don't even think i knew that i was using functions at all. but i was told to have some fun! as shown above, i accomplished that task! Looking back at this project and my knowledge of funtions, my picture shown aboves makes a lot more sense. I now know about using quadratic functions, absolute value functions, and even some sine and cosine functions. The lines above aren't just lines anymore. This project helped me understand the outcome of different functions also. Overall this was a fun project and I feel it helped me a lot. S/O to Mr.Kelly for always coming up with cool ways to learn things!
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The equations i used for this graph were: y-2x+2, y=sqrt4-2x, and y=x-2^2. To get rid of the part of the graph i didn't want to show, i had to put in "{}" x< or equal to 0, 0 < or equal to 0 < or equal to 2, and x > or equal to 2. Putting those along with their equation made the part of the graph i didnt want to show disappear. Creating a piecewise function.
Today in class we are trying to determine if the basketball in the picture above will go into the hoop or not. My prediction was that the basketball would go in, just from looking at the picture. After putting the picture the in geogebra on a graph, i started to second guess my prediction. We plotted the points using the basketballs as the points on my graph above. Then the basketballs make prabola graph. In conclusion, I think
Today our teacher showed us a video of a skateboard going down a ramp into his driveway. There were three different ramps used. A 21, 14,and 7 inch ramp. After watching the video we were told to predict the graph for the skateboard for each video. As shown above, my predictions were not close in the beginning but towards the end I got better at predicting. In my 21 in ramp, I knew the graph was suppose to go to 65 feet from watching the video. I didn't know how quickly it was going, but the skateboard moved more quickly than I had predicted. In my 14 inch and 7 in graphs my predictions got a lot closer. The 21 inch graph has a higher maximum than the 14 inch and 14 inch ramps. As the ramps get smaller, the minimum does too, although the 7 inch ramp doesn't even have a minimum. The domain for the 21 in ramp was [0-37], and the range was [0-66]. For the 14 in ramp graph the domain [0-36] and the range is [0-55]. The 7 in ramps domain was [0-15] and the range was [0-43]. When looking at all three graphs they all contain a maximum, but each maximum is different. All three graphs start at zero, therefore their minimums are zero. For example, the maximums of the 14 in ramps and the 7 in ramps are 55, and 43ft. The 21 in ramp has the biggest maximum because the ramp is higher and that causes the skateboard to move progressively faster. The graph is rising the fastest in the 21 in ramp because the ramp is higher than the other two. In all three of the graphs, they rise quite quickly, and at their own speeds as the ramp gets smaller but decelerate at the same speed because it's the same driveway .
Recently in Pre-Calc we have been learning about inverse functions! This activity helped me understand them a lot better. Our math teacher came up with this cool idea to teach us in a different way by using a piece of plastic paper, dry erase marker and a ruler. We as a class used the function "y=x^2." To find the inverse of this function you have to change all of your x's to y's. Then, take the square root of the entire function. We originally graphed the function "y=x^2," then graphed the second function. We then graphed y=x on our plastic sheet making a dotted line. After all that, we then folded our plastic sheet on the dotted line and our two graphs lined up. My whole class was amazed by this. In the end, the inverse function was not a function. It did not pass the verticle line test. Although functions can also have an inverse that is a function. It is possible. For example, y=x. overall, I really like this project and it made me understand inverse functions better and how they work!
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