Unformatted text preview: 12] × [0, 0.25]. What do you see? 260 Rational Functions 4. Graph the following rational functions by applying transformations to the graph of y =
(b) g (x) = 1 −
(a) f (x) = 1
x −2x + 1
3x − 7
(d) j (x) =
(Hint: Long division)
(c) h(x) = ax + b
. What restrictions must
cx + d
be placed on a, b, c and d so that the graph is indeed a transformation of y = ?
Discuss with your classmates how you would graph f (x) = 3 5. In Example 3.1.1 in Section 3.1 we showed that p(x) = 4x+x is not a polynomial even though
its formula reduced to 4 + x2 for x = 0. However, it is a rational function similar to those
studied in the section. With the help of your classmates, graph p(x).
x4 − 8x3 + 24x2 − 72x + 135
. With the help of your classmates, ﬁnd the x- and
x3 − 9x2 + 15x − 7
y - intercepts of the graph of g . Find the intervals on which the function is increasing, the
intervals on which it is decreasing and the local extrema. Find all of the asymptotes...
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