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Unformatted text preview: get h(x) ≈ (−1)(very 1small (+)) = very small (−). This gives us
that as x → −1+ , h(x) → 0− , so the graph is a little bit lower than (−1, 0) here.
Graphically, we have
y −3 x 5. For end behavior, we note that the degree of the numerator of h(x), 2x3 + 5x2 + 4x + 1 is 3,
and the degree of the denominator, x2 + 3x + 2, is 2. Theorem 4.2 is of no help here, since the
degree of the numerator is greater than the degree of the denominator. That won’t stop us,
however, in our analysis. Since for end behavior we are considering values of x as x → ±∞,
we are far enough away from x = −1 to use the reduced formula, h(x) = (2x+1)(x+1) , x = −1.
To perform long division, we multiply out the numerator and get h(x) = 2x x+2 +1 , x = −1,
and, as a result, we rewrite h(x) = 2x − 1 + x+2 , x = −1. As in the previous example, we
focus our attention on the term generated from the remainder, x+2 .
• The behavior of y = h(x) as x → −∞: Substituting x = −1 billion into x+2 , we get the
estimate −1 billion ≈ very small (−). Hence, h(x) = 2x−1+ x+2 ≈ 2x−1+very small (−).
This means the graph of...
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