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Points, Vectors, and Functions

Points, Vectors, and Functions

Points, Vectors, and Functions: Running the Parameter Dash Quiz

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Q. Consider the parameterization x = f(t) y = g(t) 0≤ t ≤ M where M is a constant greater than zero. Which of the following is the parameter?


x
y
M
t
Q. The point (4,32) is on the graph of which set of parametric equations?


x = 2ty = t2

x = t2, y = 2t

Q. Which of the following points is on the graph of the parametric equations 

for t ≥ 0 ?



(-1,0)
(-1,2)
(5,0)
(5,2)
Q. Determine which picture best represents the graph of the parametric equations x = 2t2 and y = t2/2  for -4 ≤ t ≤ 4.


Q. Consider the following parameterizations.

I. x = cos t, y = sin t, 0≤ ≤ 2π

II. 

III. 

IV. 



(I) and (II)
(I) and (IV)
(II) and (III)
(II) and (IV)
Q. Determine which set of parametric equations traces the unit circle clockwise exactly once for 0≤ t ≤ 3π, starting at the point (1,0) when t = 0.



Q. All the following sets of parametric equations produce the same line, except for one. Which set of equations does not produce the same line as the others?


x = -6 + 6t, y = 2t

x = -6t, y = 2-2t

x = -6 + 2t, y = 2 + 6t

Q. Which parameterization produces the ray shown below?



x = -2 + 2t, y = -3 + 3t

x = 2-2t, y = 3-3t

x = -2 + 2t, y = -3 + 3t, t≥ 0

x = 2-2t, y = 3-3t, t≥ 0

Q. With the "usual" parameterization of the unit circle, x = cos t y = sin t, which bounds on t are needed to trace exactly half the circle?


0≤ t ≤ π

0≤ t ≤ 2π

Q. Parameterize the line segment between the points (2,4) and (5,8).


x = 2 + 5t, y = 4 + 8t, 0≤ t ≤ 1

x = 5-2t, y = 8-4t, 0≤ t ≤ 1
x = 5-3t, y = 8 + 4t, 0≤ t ≤ 1
x = 2 + 3t, y = 4 + 4t, 0≤ t ≤ 1
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