The graph of y f x is the reflection of the graph of y f x across the y axis If

The graph of y f x is the reflection of the graph of

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The graph of y = f ( x ) is the reflection of the graph of y = f ( x ) across the y -axis. If a point ( x , y ) is on the graph of y = f ( x ), then ( x , y ) is on the graph of y = f ( x ), and ( x , y ) is on the graph of y = f ( x ). 4.
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7. Example: Reflect the graph y = 3 x 3 4 x 2 across the x- axis. 2 -2 -4
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8. Example: Reflect the graph y = x 3 2 x 2 across the y- axis. 2 -2 -4
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Vertical Stretching and Shrinking The graph of y = af ( x ) can be obtained from the graph of y = f ( x ) by stretching vertically for | a | > 1, or shrinking vertically for 0 < | a | < 1. For a < 0, the graph is also reflected across the x -axis. (The y -coordinates of the graph of y = af ( x ) can be obtained by multiplying the y -coordinates of y = f ( x ) by a .) 9.
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10. Example: Vertically stretch y = x 3 x vertically by 2. 2 -2 -4
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11. Example: Vertically shrink 2 by y = x 3 x . 2 -2 -4
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12. Example: Vertically stretch by 2 and reflect y = x 3 x across the x -axis 2 -2 -4
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