3. There are other graph transformations besides the ones we've considered - you can probably think of some. Using Desmos.com or your favorite graphing utility, try the following experiment: 2 Graph y = x. Then, on the same axes, plot the graph – x +y = (x+ y). This is a (very messy looking) graph transformation! I'm replacing y with - x+ y and replacing x with x+ y. Can you see what effect this transformation had on the graph? To confirm your guess, pick another graph you like and perform the same transformation. Sketch the results as well as giving your conjecture as to what this trans- formation does. Later in the term we'll be able to understand where this formula came from!

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Maximization

Have you ever seen a bridge in the shape of a parabola? Where is its maximum on the bridge? The maximum of that bridge is the highest point on that bridge. The process of finding the maximum of the bridge here is called the maximization.