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Unformatted text preview: MATH 191, Sections 1 and 3 Calculus I Fall 2007 Section 1.3: Building New Functions from Old There are a number of ways of constructing new functions from old ones. Today we consider some simple ways of doing this. Shifting. Given a function f , its easy to come up with functions whose graphs are shifted vertically or horizontally from that of f . Suppose c > is some constant. Then... 1. y = shifts the graph c units upward . 2. y = shifts the graph c units downward . 3. y = shifts the graph c units to the left . 4. y = shifts the graph c units to the right . Example. Find (and graph below!) functions which shift y = x 2 , 5 units in any given direction. Then fund the formula for a function which shifts the graph simultaneously 2 units to the left and 4 units downward. Stretching. We can just as easily stretch or compress (different kinds of scaling in a graph) a function by some factor c > 1. To......
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- Fall '07