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Stitz-Zeager_College_Algebra_e-book

Now it may well happen that in the previous scenario

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Unformatted text preview: f (x) = 3 x is given below on the left and the graph of y = g (x) is given on the right. Find a formula for g based on transformations of the graph of f . Check your answer by conﬁrming that the points shown on the graph of g satisfy the equation y = g (x). y y 5 5 4 4 3 3 2 2 1 −11 10 9 −8 −7 −6 −5 −4 −3 −2 −1 −− −1 1 1 2 3 4 5 6 7 8 x −11 10 9 −8 −7 −6 −5 −4 −3 −2 −1 −− −1 −2 4 5 6 7 8 x −4 −5 3 −3 −4 2 −2 −3 1 −5 √ y= 3x y = g (x) 5. For many common functions, the properties of algebra make a horizontal scaling the same as a vertical scaling by (possibly) a diﬀerent factor. For example, we stated earlier that √ √ 9x = 3 x. With the help of your classmates, ﬁnd the equivalent vertical scaling produced √ 2 by the horizontal scalings y = (2x)3 , y = |5x|, y = 3 27x and y = 1 x . What about 2 √ 2 y = (−2x)3 , y = | − 5x|, y = 3 −27x and y = − 1 x ? 2 106 Relations and Functions 6. We mentioned earlier in the sec...
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