Section 3.4 class notes_1

# Section 3.4 class notes_1 - Reflection of Functions about...

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Section 3.4 Transformations of Functions Objective 1: Using Vertical Shifts to Graph Functions Vertical Shifts of Functions If c is a positive real number: The graph of ( ) y f x c = + is obtained by shifting the graph of ( ) y f x = vertically upward c units. The graph of ( ) y f x c = - is obtained by shifting the graph of ( ) y f x = vertically downward c units. Objective 2: Using Horizontal Shifts to Graph Functions Horizontal Shifts of Functions If c is a positive real number: The graph of ( ) y f x c = + is obtained by shifting the graph of ( ) y f x = horizontally to the left c units. The graph of ( ) y f x c = - is obtained by shifting the graph of ( ) y f x = horizontally to the right c units. For 0 c , the graph of ( ) y f x c = - is the graph of f shifted to the right c units. At first glance, it appears that the rule for horizontal shifts is the opposite of what seems natural. Substituting x c + for x causes the graph of ( ) y f x = to be shifted to the left while substituting x c - for x causes the graph to shift to the right c units. Objective 3: Using Reflections to Graph Functions

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Unformatted text preview: Reflection of Functions about the x-Axis The graph of ( ) y f x = -is obtained by reflecting the graph of ( ) y f x = about the x-axis. Reflections of Functions about the y-Axis The graph of ( ) y f x =-is obtained by reflecting the graph of ( ) y f x = about the y-axis. Objective 4: Using Vertical Stretches and Compressions to Graph Functions Vertical Stretches and Compressions of Functions Suppose a is a positive real number: The graph of ( ) y af x = is obtained by the multiplying each y-coordinate of ( ) y f x = by a . If 1 a , the graph of ( ) y af x = is a vertical stretch of the graph of ( ) y f x = . If 0 1 a &lt; &lt; , the graph of ( ) y af x = is a vertical compression of the graph of ( ) y f x = . 3.4.17 and 27 and 41 and 53 Use the graph of a basic function and a combination of transformations to sketch each of the functions. _________________________________...
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## Section 3.4 class notes_1 - Reflection of Functions about...

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