Stitz-Zeager_College_Algebra_e-book

# Solving ac x 100 means we are trying to nd how many

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Unformatted text preview: Keeping in mind g (x) = (2x−3)(x+2) , we proceed to our ( analysis near each of these values. • The behavior of y = g (x) as x → −2: As x → −2− , we imagine substituting a number a little bit less than −2. We have g (x) ≈ 9 (−9)(−1) 9 ≈ ≈ very big (+) (−5)(very small (−)) very small (+) And Jeﬀ doesn’t think much of it to begin with... 252 Rational Functions so as x → −2− , g (x) → ∞. On the ﬂip side, as x → −2+ , we get g (x) 9 ≈ very big (−) very small (−) so g (x) → −∞. • The behavior of y = g (x) as x → 3: As x → 3− , we imagine plugging in a number just shy of 3. We have g (x) ≈ 4 (1)(4) ≈ ≈ very big (−) ( very small (−))(5) very small (−) Hence, as x → 3− , g (x) → −∞. As x → 3+ , we get g (x) ≈ 4 ≈ very big (+) very small (+) so g (x) → ∞. Graphically, we have (again, without labels on the y -axis) y −3 −1 1 2 4 x 5. Since the degrees of the numerator and denominator of g (x) are the same, we know from Theorem 4.2 that we can ﬁnd the horizontal asymptote of...
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