Trigonometry Workbook For Dummies
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When you apply a vertical transformation to a parent graph, you are stretching or shrinking the graph along the y-axis, which changes its height. A number (or coefficient) multiplying in front of a function causes the vertical transformation. The coefficient always affects the height of each and every point in the graph of the function. We call the vertical transformation a stretch if the coefficient is greater than 1 and a shrink if the coefficient is between 0 and 1.

For example, the graph of f(x) = 2x2 takes the graph of f(x) = x2 and stretches it by a vertical factor of two. That means that each time you plot a point vertically on the graph, the value gets multiplied by two (making the graph twice as tall at each point). For example, in f(x)=x2, 1 gets mapped to 2×12=2, 2 gets mapped to 2×22=8, 3 gets mapped to 2×32=18, etc.

The vertical transformation of f(x) = 2x2 and


are shown in this figure.


The transformation rules apply to any function, so the vertical transformation of


is shown here.


The 4 is a vertical stretch; it makes the graph four times as tall at every point. For example, 1 gets mapped to 4×sqrt(1)=4, 4 gets mapped to 4×sqrt(4)=8, 9 gets mapped to 4×sqrt(9)=12, etc. (notice that this example uses numbers that you can easily take the square root of to make graphing a simple task); and so on.

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Mary Jane Sterling taught algebra, business calculus, geometry, and finite mathematics at Bradley University in Peoria, Illinois, for more than 30 years. She is the author of several For Dummies books, including Algebra Workbook For Dummies, Algebra II For Dummies, and Algebra II Workbook For Dummies.

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