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# Mth141S23n - Sec 2.3 Stretching Shrinking and Reflecting...

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Sec. 2.3 – Stretching, Shrinking, and Reflecting Graphs Stretching/Shrinking multiplying or dividing by a value See class handout!! Ex. f(x) = | x | g(x) = 3 | x | we are multiplying the basic graph by 3 (and the 3 is outside the absolute value operation), this will multiply the y-value of each point by 3 or stretch the graph vertically FROM THE X-AXIS by a factor of 3!! Ex. f(x) = 1 3 x or 3 x Here we are dividing the y-coordinate of each point by 3! Which will “contract” (“shrink”) the graph vertically towards the x-axis . Outside change : 2 ( ) f x x = and 2 ( ) 3 g x x = . Since the 3 is outside the squaring operation, this will stretch the graph vertically by a factor of 3 from the x-axis .

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Inside change : 2 ( ) f x x = and 2 ( ) (3 ) g x x = . Since the 3 is inside the squaring operation, this will affect the graph horizontally and the affect will be the opposite of multiplying by 3, i.e. it will contract the graph horizontally by a factor of 3 towards the y-axis. (Horizontal changes work “’backwards”! Vertical changes work “normally”’!)
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