Stitz-Zeager_College_Algebra_e-book

We have 3 being added to an input indicating a

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Unformatted text preview: from, the output of a function causes the graph to shift up or down, respectively”. So what happens if we add to or subtract from the input of the function? Keeping with the graph of y = f (x) above, suppose we wanted to graph g (x) = f (x + 2). In other words, we are looking to see what happens when we add 2 to the input of the function.1 Let’s try to generate a table of values of g based on those we know for f . We quickly find that we run into some difficulties. 1 We have spent a lot of time in this text showing you that f (x + 2) and f (x) + 2 are, in general, wildly different algebraic animals. We will see momentarily that the geometry is also dramatically different. 86 Relations and Functions x 0 2 4 5 (x, f (x)) f (x) g (x) = f (x + 2) (x, g (x)) (0, 1) 1 f (0 + 2) = f (2) = 3 (0, 3) (2, 3) 3 f (2 + 2) = f (4) = 3 (2, 3) (4, 3) 3 f (4 + 2) = f (6) =? (5, 5) 5 f (5 + 2) = f (7) =? When we substitute x = 4 into the formula g (x) = f (x + 2), we are asked to find f (4 + 2) = f (6) which doesn’t exist bec...
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This note was uploaded on 05/03/2013 for the course MATH Algebra taught by Professor Wong during the Fall '13 term at Chicago Academy High School.

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