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Stitz-Zeager_College_Algebra_e-book

1 which amounts to multiplying them by 10 to obtain

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Unformatted text preview: pun? In most other cases, though, rational√ exponents are preferred. 5 As mentioned in Section 2.2, f (x) = x2 = |x| so that absolute value is also considered an algebraic functions. 4 314 Further Topics in Functions √ f (x) 3x 3 2 − x 3x = 0 x=0 x=0 x=0 = = or or or or 0 0 √ 3 2−x=0 √ 3 3 2 − x = 03 2−x=0 x=2 The zeros 0 and 2 divide the real number line into three test intervals. The sign diagram and accompanying graph are below. Note that the intervals on which f is (+) correspond to where the graph of f is above the x-axis, and where the graph of f is below the x-axis we have that f is (−). The calculator suggests something mysterious happens near x = 2. Zooming in shows the graph becomes nearly vertical there. You’ll have to wait until Calculus to fully understand this phenomenon. (−) 0 (+) 0 (−) 0 2 y = f (x) y = f (x) near x = 2. √ 2. In g (x) = 2 − 4 x + 3, we have two radicals both of which are even indexed. To satisfy √ √ √ 4 x + 3, we require x + 3 ≥ 0 or x ≥ −3. To satisfy 2 − 4 x + 3, we n...
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