1 2x2 x x2 domain 1 1 2 2 vertical asymptote

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Unformatted text preview: e graphs of rational functions. Consider the function f (x) = 2x+11 from Example 4.1.1. Using a graphing calculator, we obtain 1 You should review Sections 1.2 and 1.4 if this statement caught you off guard. 234 Rational Functions Two behaviors of the graph are worthy of further discussion. First, note that the graph appears to ‘break’ at x = −1. We know from our last example that x = −1 is not in the domain of f which means f (−1) is undefined. When we make a table of values to study the behavior of f near x = −1 we see that we can get ‘near’ x = −1 from two directions. We can choose values a little less than −1, for example x = −1.1, x = −1.01, x = −1.001, and so on. These values are said to ‘approach −1 from the left.’ Similarly, the values x = −0.9, x = −0.99, x = −0.999, etc., are said to ‘approach −1 from the right.’ If we make two tables, we find that the numerical results confirm what we see graphically. x −1.1 −1.01 −1.001 −1.0001 f (x) (x, f (x)) 32 (−1.1, 32) 302 (−1.01, 302) 3002 (−1.001, 30...
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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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