Stitz-Zeager_College_Algebra_e-book

If it is negative we say the line is decreasing a

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Unformatted text preview: unit −− − − − −→ −−−−−− add 1 to each x-coordinate y = g2 (x) = −x2 y = g3 (x) = g2 (x − 1) = −x2 + 2x − 3 −2 horizontal stretch by a factor of 2 −− − − − − − − −→ −−−−−−−−− multiply each x-coordinate by 2 y = g3 (x) = −x2 + 2x − 3 y = g (x) = g3 1 2x = − 1 x2 + x − 3 4 We have kept the viewing window the same in all of the graphs above. This had the undesirable consequence of making the last graph look ‘incomplete’ in that we cannot see the original shape of f (x) = x2 . Altering the viewing window results in a more complete graph of the transformed function as seen below. y = g (x) This example brings our first chapter to a close. In the chapters which lie ahead, be on the lookout for the concepts developed here to resurface as we study different families of functions. 104 1.8.1 Relations and Functions Exercises 1. The complete graph of y = f (x) is given below. Use it to graph the following functions. y (0, 4)...
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