Stitz-Zeager_College_Algebra_e-book

To graph g x af bx h k 1 subtract h from each of

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Unformatted text preview: is on the graph of f , then f (a) = b. Hence g a = f 2 · a = f (a) = b so that 2 2 a 2 , b is on the graph of g . In other words, to graph g we divide the x-coordinates of the points on the graph of f by 2. This results in a horizontal scaling9 by a factor of 1 . 2 y y 5 ,5 2 (5, 5) 5 5 4 4 (2, 3) (1, 3) 3 3 (4, 3) (2, 3) 2 2 (0, 1) (0, 1) 1 2 3 y = f (x) 4 5 x horizontal scaling by a factor of 1 2 1 2 3 4 5 −− − − − − − − − −→ −−−−−−−−−− multiply each x-coordinate by 1 2 x y = g (x) = f (2x) If, on the other hand, we wish to graph y = f 1 x , we end up multiplying the x-coordinates 2 of the points on the graph of f by 2 which results in a horizontal scaling10 by a factor of 2, as demonstrated below. 9 10 Also called ‘horizontal shrink,’‘horizontal compression’ or ‘horizontal contraction’ by a factor of 2. Also called ‘horizontal stretch,’‘horizontal expansion’ or ‘horizontal dilation’ by a factor of 2. 96 Relations and Functions y y (10, 5) (5, 5) 5 5 4 4 (4, 3) (2, 3) 3 3 (8, 3) (4, 3) 2 2 (0, 1) (0, 1) 1 2 3...
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