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3.5 The Graph Scale-Change Theorem Functions, Statistics, and Trigonometry Name: _______________________ Warm-Up: Recall what a scale-change is from geometry. Write a brief description and check with your neighbor. Essential Question: What is a scale change and what are the effects on our pre-image graph? Vocabulary: Scale Change: ________________________________________________________________ ____________________________________________________________________________________ Horizontal Scale Factor: ______________________________________________________________ Vertical Scale Factor: _________________________________________________________________ Size Change: ________________________________________________________________________ ** Scale changes do NOT produce congruent figures. Graph Scale-Change Theorem: In a relation described by a sentence in x and y, the following two processes yield the same graph: (1) replacing x by x y and y by in the equation; a b (2) applying the scale change (x, y) --> (ax, by) to the graph of the original relation € € Example 1: Compare the graphs of y = x and y = 6x . € € Example 2: Sketch the graph of y = 6x . 4 € Negative Scale Factors: _____________________________________________________________________ Which axis? Example 3: Sketch the image of y = x3 under S(x, y) = (-2x, y). Give an equation for the image. Example 4: The line 41x – 29y = 700 contains the point (39, 31) and (10, -10). Use this information to obtain two points on the line with equation 20.5x – 87y = 700.