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Section 2_4 - Math 1650 Lecture Notes Jason Snyder PhD...

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Math 1650 Lecture Notes §2.4 Jason Snyder, PhD. Transformations of Functions Page 1 of 8 § 2.4: Transformations of Functions Vertical Shifting Adding a constant to a function shifts its graph vertically: upward if the constant is positive and downward if the constant is negative. Example 1 Vertical Shifts of Graphs Use the graph of ? ? = ? 2 to sketch the graph of each function. (a) ? ? = ? 2 + 2 (b) ? ? = ? 2 3 x y Vertical Shifts of Graphs Suppose c > 0. To graph ? = ? ? + 𝑐 , shift the graph of ? = ? ? upward c units. To graph ? = ? ? − 𝑐 , shift the graph of ? = ? ? downward c units.
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Math 1650 Lecture Notes §2.4 Jason Snyder, PhD. Transformations of Functions Page 2 of 8 Example 2 Vertical Shifts of Graphs Use the graph of ? ? = ? 3 5 ? , which is sketched below, to sketch the graph of each of the following. (a) ? ? = ? 3 5 ? + 3 (b) ? ? = ? 3 5 ? − 2 x y Horizontal Shifting Suppose we have the graph of ? = ? ( ? ) , how would we use this graph to sketch the graphs of ? = ? ( ? + 𝑐 ) and ? = ? ? − 𝑐 , where c > 0? The y value of ? ( ? − 𝑐 ) is the same as ? ( ? ) evaluated at x c . Since x c is c units to the left of x
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