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Linear Transformations Worksheet

Linear Transformations Worksheet

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Professor Dave again, let’s transform some functions. We just learned how to graph some basic functions, like F of X equals X squared. This is a parabola that opens in the positive direction, with its vertex at the origin. But functions are rarely this simple. What if we want to graph X squared plus two? Or X plus two quantity squared? Or two X squared? In each case, we could do one of two things. We could make a table and find some ordered pairs to plot, or we could recognize how the number two is transforming the graph of X squared in a different way for each case. Let’s make some tables and I’ll show you what I mean. Take the first example, X squared plus two. Let’s plug in the values we would typically use when evaluating X squared, and we can see that in each case, we simply add two to what we would have gotten normally. If the function is two greater, then it sits two units higher on the graph. So when we add or subtract a number in this way, we are producing a vertical s

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