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Unformatted text preview: C01S03.032: The graph starts with two “bends” when c = −5. As c increases the bends become narrower
and narrower and disappear when c = 0. Then the graph gets steeper and steeper. See the following ﬁgure. 15 c=5
c = –5 10
5 4 2 2 4 5
10 C01S03.033: The graph always passes through (0, 0) and is tangent to the xaxis there. When c = −5
there is another zero at x = 5. As c increases this zero shifts to the left until it coincides with the one at
x = 0 when c = 0. At this point the “bend” in the graph disappears. As c increases from 1 to 5, the bend
reappears to the left of the xaxis and the second zero reappears at −c. C01S03.034: The graph is always tangent to the xaxis at x = 0 and is always symmetric around the
y axis. When c = −5 there is another pair of zeros near ± 2.2. As c increases these zeros move closer to
x = 0 and the bends in the graph get smaller and smaller. They disappear when c = 0 and, at the same
time, the zeros merge with the one at x = 0. Thereafter the graph simply becomes steeper and steeper. See
the following ﬁgure. c=5
15 10 5 c = –5
3 2 1 1 2 3 5 C01S03.035: The graph is always symmetric around the origin (and, consequently, always passes through
the origin). When c = −5 there is another pair of zeros near ± 2.2. As c increases the graph develops positive
slope at x = 0, two more bends, and two more zeros on either side of the origin. They move outward and,
when c = −2, they coincide with the outer pair of zeros, which have also been moving toward the origin.
They reach the origin when c = 0 and thereafter the graph simply becomes steeper and steeper. C01S03.036: As c increases the “mountain” around the y axis gets narrower and steeper. See the following
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 Spring '11
 CHENG
 Calculus

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