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**Unformatted text preview: **nce its domain is all real numbers
and it has no zeros. Our sole test interval is (−∞, ∞), and since we know r(0) = 1, we
conclude r(x) is (+) for all real numbers. At this point, we don’t have much to go on for
a graph. Below is a comparison of what we have determined analytically versus what the
calculator shows us. We have no way to detect the relative extrema analytically15 apart from
brute force plotting of points, which is done more eﬃciently by the calculator.
6 y 5
4
3
2
1 −3 15 −1 1 2 Without appealing to Calculus, of course. 3
x 4.2 Graphs of Rational Functions 4.2.1 259 Exercises 1. Find the slant asymptote of the graph of the rational function.
x3 − 3x + 1
x2 + 1
2 + 5x − 3
2x
(b) f (x) =
3x + 2
(a) f (x) = −5x4 − 3x3 + x2 − 10
x3 − 3x2 + 3x − 1
−x3 + 4x
(d) f (x) =
x2 − 9
(c) f (x) = 2. Use the six-step procedure to graph each rational function given. Be sure to draw any
asymptotes as dashed lines.
(a) f (x) =
(b) f (x) =
(c) f (x) =
(d) f (x) =
(...

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