Stitz-Zeager_College_Algebra_e-book

Stitz-Zeager_College_Algebra_e-book

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Unformatted text preview: other transformations introduced in this section. √ Example 1.8.3. Let f (x) = x. Use the graph of f from Example 1.8.1 to graph the following functions below. Also, state their domains and ranges. √ 1. g (x) = 3 x 2. j (x) = √ 9x 3. m(x) = 1 − x+3 2 Solution. 1. First we note that the domain of g is [0, ∞) for the usual reason. Next, we have g (x) = 3f (x) so by Theorem 1.5, we obtain the graph of g by multiplying all of the y -coordinates of the points on the graph of f by 3. The result is a vertical scaling of the graph of f by a factor of 3. We nd the range of g is also [0, ∞). 1.8 Transformations 97 y y (4, 6) 6 6 5 5 4 4 3 3 (1, 3) (4, 2) 2 2 (1, 1) 1 1 (0, 0) (0, 0) 1 2 3 y = f (x) = √ 4 x 1 vertical scale by a factor of 3 2 3 x multiply each y -coordinate by 3 x 4 −− − − − − − − − − − − − − − − − − − − −→ √ y = g (x) = 3f (x) = 3 x 2. To determine the domain of j , we solve 9x ≥ 0 to find x ≥ 0. Our domain is once a...
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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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