A
I
B
II
C
III
D
IV
E
V
1. The graphs in the left column are simultaneous cartesian graphs of two functions x = x(t), y = y(t)for t in an interval [a, b]. The parametric curves C: (x, y)=(x(t), y(t)) of these pairs are on the right. Match the graphs on the right with those on the left. Then using arrows, indicate how the parametric curve is traced out as t increases on its domain
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A
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I
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B
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II
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C
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III
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D
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IV
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E
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V
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Solution:
Start with B. All the values of x and y are
³ 0 so the parametric graph will be in the first quadrant. Graph IV is the only one on the right that has this property, so B corresponds to IV.In D all the y values are
³ 0 so D corresponds to IIIn E, dx/dt = 0 (without dy/dt being 0) 3 times so the corresponding parametric curve has 3 vertical tangent. So E corresponds to III
In A dx/dt = 0 (without dy/dt being 0) 2 times si the matching parametric curve has 2 vertical tangents. So A corrsponds to V
By elimimation C corresonds to I.
The "paths traveled are indicated below
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