Stitz-Zeager_College_Algebra_e-book

A ax xx 22 x 0 multiplicity 1 x 2 multiplicity

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Unformatted text preview: x − 3)2 (x + 2) x2 + 1 = 0. We get x = 0, x = 3, and x = −2. (The equation x2 + 1 = 0 produces no real solutions.) These three points divide the real number line into four intervals: (−∞, −2), (−2, 0), (0, 3) and (3, ∞). We select the test values x = −3, x = −1, x = 1, and x = 4. We find f (−3) is (+), f (−1) is (−) and f (1) is (+) as is f (4). Wherever f is (+), its graph is above the x-axis; wherever f is (−), its graph is below the x-axis. The x-intercepts of the graph of f are (−2, 0), (0, 0) and (3, 0). Knowing f is smooth and continuous allows us to sketch its graph. y (+) 0 (−) 0 (+) 0 (+) −2 0 3 −3 −1 1 x 4 A sketch of y = f (x) A couple of notes about the Example 3.1.5 are in order. First, note that we purposefully did not label the y -axis in the sketch of the graph of y = f (x). This is because the sign diagram gives us the zeros and the relative position of the graph - it doesn’t give us any information as to how high or low the graph strays from the...
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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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