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?
Q. The point (4,32) is on the graph of which set of parametric equations?
x = 2t, y = t2
x = t2, y = 2t
Q. Which of the following points is on the graph of the parametric equations
for t ≥ 0 ?
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≤ t ≤ 2π
(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