What type of function does this data appear to follow? The data appears to follow an exponential function. Please enter some estimated points from the graph into Desmos.com or Geogbra.org to determine an estimated mathematical model for this function. Y=1.9^(.9x-3.3)+-.1 What is the domain of this function?
The domain is all real numbers. What is the range of this function? The range is x>0Please read the following article and comment on the future shape of your mathematical model: It will continue to increase exponentially as new products are released. How does this affect your predictions of domain and range of the function? Is there a problem with trying to extend a set of data points to continuous functions? Why or why not? This leads me to the conclusion that the range could fall into the negative and and the domain would not continue to increase as expected. You cannot extend this information for longer periods of time because the graph cannot always be properly predicted.
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A. What do you need to know to make an equation for the flight of the ball?
You need certain checkpoints (found in the picture), a line of best fit, and try to find a trend in distance between each ball. B. Will the shot go in? According to my image and equation, the shot will go in. This is j A. How close was your prediction to the actual graph? If your graphs were different then why were they different? What initial reasoning led you to your original graph and why was it different?
MY first graph was pretty far off. I had the wrong idea when it came to finding out that the skateboard would go backwards as fast as it did. My reasoning was that the speeding up would be a gradual process and that it wouldn't happen as quickly as it did. This caused the slope early on in my function to be too low and continue for too long. B. What do the zeros of your graph represent? Zeros represent when the skateboard isn't moving. C. How do the three graphs compare in terms of zeros, maximums and minimums? What's similar and different and why? They all start at zero. The higher the ramp, the higher the maximum and the longer it takes to get back to zero. None of them have minimums lower than zero because you can't go a negative distance. The higher the ramp, the greater the accelerating force, which makes the skateboard go faster, which causes the trends above. D. Consider the slopes of the graphs. When is the graph rising the fastest and what does it mean? When is it falling the fastest and what does it mean? The graph is rising the fastest shortly after the skateboard gets off the ramp. This also happens to be the time the slope is the highest. This means the object gains its maximum velocity shortly after being accelerated. The farther you get from the maximum, the faster the slope goes down. This is because it is gathering momentum from the hill it is going down backwards. E. Please be sure to add an image of your graph(s) and contextualize the blog post for your readers. https://drive.google.com/folderview?id=0B9eadWLsDcAqS0VRQ1ZuMFVweW8&usp=sharing A. He raised the flag at a constant rate
B. He got less efficient as time went on - Most realistic because after a little bit of pulling his arms would probably get tired and he would slow down. C. His speed of raising changed back and forth quite often D. He got more efficient as time went on E. He sped up rapidly then slowed back down F. The flag went up instantly - Least realistic because it isn't humanly possible to pull a flag that far instanly For the eyes I used constant functions at 20 on the Y axis. I used brackets and the greater than or less than signs to create a line segment rather than a line that continues infinitely. By setting the line as (#>x>#), the line will remain in between those two numbers. For the mouth, I used a quadratic function. By decreasing the coefficient of x, I was able to make the parabola wider than the standard y=x^2. I had to do the same thing for this as I did with the eyes in terms of keeping the length of the segment limited. I changed the Y value to lower it as well. I used a conic to make the outline of the head. I changed the b value to make the circle either more wide or narrow.
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