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Stitz-Zeager_College_Algebra_e-book

# When we go to nd the zeros of f we nd to our chagrin

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Unformatted text preview: The next example motivates the core ideas. Example 2.4.1. Let f (x) = 2x − 1 and g (x) = 5. 1. Solve f (x) = g (x). 2. Solve f (x) < g (x). 3. Solve f (x) > g (x). 4. Graph y = f (x) and y = g (x) on the same set of axes and interpret your solutions to parts 1 through 3 above. Solution. 1. To solve f (x) = g (x), we replace f (x) with 2x − 1 and g (x) with 5 to get 2x − 1 = 5. Solving for x, we get x = 3. 2. The inequality f (x) < g (x) is equivalent to 2x − 1 < 5. Solving gives x < 3 or (−∞, 3). 3. To ﬁnd where f (x) > g (x), we solve 2x − 1 > 5. We get x > 3, or (3, ∞). 4. To graph y = f (x), we graph y = 2x − 1, which is a line with a y -intercept of (0, −1) and a slope of 2. The graph of y = g (x) is y = 5 which is a horizontal line through (0, 5). y 8 7 6 y = g ( x) 5 4 3 2 y = f (x) 1 1 2 3 4 x −1 To see the connection between the graph and the algebra, we recall the Fundamental Graphing Principle for Functions in Section 1.7: the point (a, b) is on the...
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