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Stitz-Zeager_College_Algebra_e-book

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Unformatted text preview: ‘vertical compression’ or ‘vertical contraction’ by a factor of 2. 1.8 Transformations 95 by a factor of 2’ makes sense if we are scaling something by multiplying it by 2. Similarly, we believe words like ‘shrink’, ‘compression’ and ‘contraction’ all indicate something getting smaller, so if we scale something by a factor of 1 , we would say it ‘shrinks by a factor of 2’ - not ‘shrinks by 2 a factor of 1 .’ This is why we have written the descriptions ‘stretch by a factor of a’ and ‘shrink by 2 1 a factor of a ’ in the statement of the theorem. Second, in terms of inputs and outputs, Theorem 1.5 says multiplying the outputs from a function by positive number a causes the graph to be vertically scaled by a factor of a. It is natural to ask what would happen if we multiply the inputs of a function by a positive number. This leads us to our last transformation of the section. Referring to the graph of f given at the beginning of this section, suppose we want to graph g (x) = f (2x). In...
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