Trigonometry Workbook For Dummies
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When you apply a horizontal transformation to a parent graph, you are stretching or shrinking the graph horizontally, along the x-axis. A number multiplying a variable inside a function affects the horizontal position of the graph — a little like the fast-forward or slow-motion button on a remote control, making the graph move faster or slower. A coefficient greater than 1 causes the function to shrink horizontally, making it appear to move faster. A coefficient between 0 and 1 makes the function appear to move slower, or a horizontal stretch.


For instance, look at the graph of f(x) = |2x| in the preceding figure. If the distance between any two x values in the parent graph is 1, then those x-values will correspond (based on the values they get mapped to) to x-values for the graph f(x)=|2x| having a distance of ½. To see this, set the inside of the new, transformed function equal to the distance between the x values, you get 2x = 1. Solving the equation gives you x = 1/2 Hence in the parent graph we have the points (0,0) , (1,1), (2,2), (3,3), etc.; yet in f(x)=|2x| we have the points (0,0) , (1/2,1), (1,2),(3/2.3), etc.

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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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