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Unformatted text preview: 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 &gt; 0. To graph ? = ? + , shift the graph of ? = ? upward c units. To graph ? = ? , shift the graph of ? = ? downward c units. 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 ? = ? ( + ) and ? = ? , where c &gt; 0? The y value of ? ( ) is the same as ? ( ) evaluated at x c . Since x c is c units to the left of x , it follows that the graph of...
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This note was uploaded on 10/07/2009 for the course MATH 150 taught by Professor Unknown during the Spring '06 term at Ohio State.
- Spring '06