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Stitz-Zeager_College_Algebra_e-book

# 1 1 2 3 4 5 6 7 1 2 3 4 5 6 x x x 42 graphs of

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Unformatted text preview: h we are multiplying our ‘very small (−)’ by 2, the denominator will continue to get smaller and smaller, and remain negative. The result is a fraction whose numerator is positive, but whose denominator is very small and negative. Mentally, f (x) ≈ 3 3 ≈ ≈ very big (−) 2 (very small (−)) very small (−) 3 As we mentioned at least once earlier, since functions can have at most one y -intercept, once we ﬁnd (0, 0) is on the graph, we know it is the y -intercept. 4 The sign diagram in step 6 will also determine the behavior near the vertical asymptotes. 4.2 Graphs of Rational Functions 249 The term ‘very big (−)’ means a number with a large absolute value which is negative.5 What all of this means is that as x → −2− , f (x) → −∞. Now suppose we wanted to determine the behavior of f (x) as x → −2+ . If we imagine substituting something a little larger than −2 in for x, say −1.999999, we mentally estimate f (x) ≈ −6 3 3 = ≈ ≈ very big (+) (−4...
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