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1310-Notes-Sec-34-big-filled - Math 1310 Section 3.4...

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Math 1310 Class Notes – Section 3.4, Page 1 of 16 Math 1310 Section 3.4 Transforming Functions In my opinion, this is the most important section of the semester . In future courses, you will need to be able to sketch the graph of a function quickly and accurately. You can use transformations to do this. To introduce this topic, we’ll use the function ( ) . f x x = Here is the graph of this function: Translating graphs We’ll start with translations . To translate a graph means to shift it horizontally, vertically or both. Vertical shifting: To graph ( ) , 0 y f x c c = + , start with the graph of ( ) f x and shift it upward c units. To graph ( ) , 0 y f x c c = - , start with the graph of ( ) f x and shift it downward c units.
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Math 1310 Class Notes – Section 3.4, Page 2 of 16 Horizontal shifting: To graph ( ), 0, y f x c c = + start with the graph of ( ) f x and shift it left c units. To graph ( ), 0, y f x c c = - start with the graph of ( ) f x and shift it right c units. Example 1: Sketch a graph of ( ) 2 f x x = + .
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Math 1310 Class Notes – Section 3.4, Page 3 of 16 Example 2: Sketch a graph of ( ) 3 f x x = - Example 3: Sketch a graph of ( ) 1 f x x = + .
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Math 1310 Class Notes – Section 3.4, Page 4 of 16 Example 4: Sketch a graph of ( ) 3. f x x = - Example 5: Sketch a graph of ( ) 2 1. f x x = - +
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Math 1310 Class Notes – Section 3.4, Page 5 of 16
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