Below I have put a picture of all the different situations of a boy raising a flag. Each one represents a different function for all the different ways the flag may have been raised. As you look at graph A you see that the flag was raised at an even rate over time creating a straight line up. In graph B the flag looks like it was pulled up pretty fast and near the end it started to slow down. Graph C looks like each squiggle is another stride up to raise the flag. Graph D shows that at first the flag was raising fairly slow and as it got closer to the top the flag rate became faster. In graph E the flag begins going up very slow and then speeds up and at the end slows down again. In graph F the flag gets pulled up in one pull. I think the most realistic graph would be graph C because when you pull a flag up it takes many different pulls. The most unrealistic graph would be graph F because no normal person could pull up the flag in one pull.
In the "Family of Functions" Packet I reviewed what I had previously learned in Algebra two. There are a lot of different types of functions examples of them would be quadratic, square root, cubic and logarithmic plus many more. These functions that I reviewed helped me in making my smiley faces look different. The first smiley face that is below is the one I made with not knowing what I was doing yet. I just changed numbers in the original functions and moved features on the smiley face. I also used a quadratic function to make the hair and the hat. The second time around I had reviewed all the different functions. It helped me learn and remember about all the different shapes of a graph they create. for an example a quadratic function creates a "U" shape. Depending if the number is positive or negative it could be upside down or up right. The smiley face below I made into a sunshine smile. I used a bunch of functions like "y=2x" to make the rays of the sun. The hardest part of the packet was just remembering all the functions I learned last year. I also found it challenging to remember what each number in the equation did like did it move it up or down kind of thing. The activity helped a bunch in recalling of what I previously had learned but had forgotten.
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