Mathematics 309 - the elementary geometry of wave motion
Part I - scaling and shiftingOne way of obtaining one graph from another is by scaling and shifting either x or y or both, so that the graph y=f(x) becomes the graph y = af(bx + c) + d. The way to see what happens to the graph is to understand what happens in simple steps with just one change at a time.
Only the last one is tricky, since it involves a sequence of substitutions. In order to see which ones, we unravel the process.
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