Unformatted text preview: 4 4 (2, 3) 5, 3 3 (4, 3)
(0, 1) 0,
1 2 3 y = f (x) 4 5 x vertical scaling by a factor of 1
2 1
2 4, 1 1 âˆ’âˆ’ âˆ’ âˆ’ âˆ’ âˆ’ âˆ’ âˆ’ âˆ’ âˆ’â†’
âˆ’âˆ’âˆ’âˆ’âˆ’âˆ’âˆ’âˆ’âˆ’âˆ’
multiply each y coordinate by 1
2 3
2 2, 2 2 y= 5
2 2 3 4 3
2
5 x 1
f (x)
2 These results are generalized in the following theorem.
Theorem 1.5. Vertical Scalings. Suppose f is a function and a > 0. To graph y = af (x),
multiply all of the y coordinates of the points on the graph of f by a. We say the graph of f
has been vertically scaled by a factor of a.
â€¢ If a > 1, we say the graph of f has undergone a vertical stretch (expansion, dilation) by a
factor of a.
â€¢ If 0 < a < 1, we say the graph of f has undergone a vertical shrink (compression, contraction)
1
by a factor of a .
A few remarks about Theorem 1.5 are in order. First, a note about the verbiage. To the authors, the
words â€˜stretchâ€™, â€˜expansionâ€™, and â€˜dilationâ€™ all indicate something getting bigger. Hence, â€˜stretched
8 Also called â€˜vertical shrink,â...
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 Fall '13
 Wong
 Algebra, Trigonometry, Cartesian Coordinate System, The Land, The Waves, RenÃ© Descartes, Euclidean geometry

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