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Pre1o3_1330 - y = af x is the graph of y = f x vertically...

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Section 1.3 – Transformations of Graphs 1 Section 1.3 Transformations of Graphing Library of functions (know these!!!): 2 ) ( x x f = 3 ) ( x x f = x x f = ) ( x x f = ) ( x x f 1 ) ( = 2 1 ) ( x x f = -5 -4 -3 -2 -1 1 2 3 4 -4 -3 -2 -1 1 2 3 4 x y 3 ) ( x x f = = 3 1 x -3 -2 -1 1 2 3 -3 -2 -1 1 2 3 x y
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Section 1.3 – Transformations of Graphs 2 Vertical Shifting To graph c x f y = ) ( , ( c > 0), start with the graph of ( ) f x and shift it upward c units. To graph c x f y - = ) ( , ( c > 0), start with the graph of ( ) f x and shift it downward c units. Horizontal Shifting To graph ) ( c x f y = , ( c > 0), start with the graph of ( ) f x and shift it to the left c units. To graph ) ( c x f y - = , ( c > 0), start with the graph of ( ) f x and shift it to the right c units. Reflection of Functions A reflection is the “mirror-image” of graph about the x -axis or y -axis. To graph ( ) f x - , reflect the graph of f ( x ) about the x -axis. To graph ( ) f x - , reflect the graph of f ( x ) about the y-axis. Vertical Stretching and Shrinking Vertical Stretching: If a > 1, the graph of
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Unformatted text preview: y = af ( x ) is the graph of y = f ( x ) vertically stretched by multiplying each of its y-coordinates by a . Vertical Shrinking: If 0< a < 1, the graph of y = af ( x ) is the graph of y = f ( x ) vertically shrunk by multiplying each of its y-coordinates by a . Recommended Order for Transformations 1. Vertical stretching or shrinking. 2. Reflection about the x-axis. 3. Vertical and Horizontal Translations. 4. Reflection about the y-axis. Section 1.3 – Transformations of Graphs 3 Example 1: Sketch the graph of: 2 1 ) ( +--= x x f-4-3-2-1 1 2 3 4-2-1 1 2 x y Example 2: Given y = 3f(x – 2) – 1. a. State the transformations needed, in the recommended order. ] b. Suppose (1, 2) is on the graph of f . If the function is transformed y = 3f(x – 2) – 1, where would the point (1, 2) end up?...
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