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Unformatted text preview: the function values f (x) approach the number 2.
7 240 Rational Functions
y = g (x) doesn’t appear to level oﬀ to a constant value, so there is no horizontal asymptote.8 3. The degrees of the numerator and denominator of h(x) are both three, so Theorem 4.2 tells
us y = −2 = −3 is the horizontal asymptote. The calculator conﬁrms this. The graph of y = f (x) The graph of y = g (x) The graph of y = h(x) Our last example of the section gives us a real-world application of a horizontal asymptote. Though
the population below is more accurately modeled with the functions in Chapter 6, we approximate
it9 using a rational function.
Example 4.1.5. The number of students, N , at local college who have had the ﬂu t months after
the semester begins can be modeled by the formula N (t) = 500 − 1+3t for t ≥ 0.
1. Find and interpret N (0).
2. How long will it take until 300 students will have had the ﬂu?
3. Determine the behavior of N as t → ∞. Interpret this result graphically and within the
context of the problem....
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