Stitz-Zeager_College_Algebra_e-book

Generalizing we have the following result theorem 13

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Unformatted text preview: unction g takes the output f (x) and adds 2 to it. In order to graph g , we need to graph the points (x, g (x)). How are we to find the values for g (x) without a formula for f (x)? The answer is that we don’t need a formula for f (x), we just need the values of f (x). The values of f (x) are the y values on the graph of y = f (x). For example, using the points indicated on the graph of f , we can make the following table. x 0 2 4 5 (x, f (x)) f (x) g (x) = f (x) + 2 (x, g (x)) (0, 1) 1 3 (0, 3) (2, 3) 3 5 (2, 5) (4, 3) 3 5 (4, 5) (5, 5) 5 7 (5, 7) In general, if (a, b) is on the graph of y = f (x), then f (a) = b, so g (a) = f (a) + 2 = b + 2. Hence, (a, b +2) is on the graph of g . In other words, to obtain the graph of g , we add 2 to the y -coordinate of each point on the graph of f . Geometrically, adding 2 to the y -coordinate of a point moves the point 2 units above its previous location. Adding 2 to every y -coordinate on a graph en masse is usually described as ‘shifting the graph u...
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