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Points, Vectors, and Functions

Points, Vectors, and Functions

Points, Vectors, and Functions: Running the Parameter Dash True or False

1. 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
2. The point (4,32) is on the graph of which set of parametric equations?
3. Which of the following points is on the graph of the parametric equations 

for t ≥ 0 ?(5,2)

4. Determine which picture best represents the graph of the parametric equations x = 2t2 and y = t2/2  for -4 ≤ t ≤ 4.
5. Consider the following parameterizations.

I. x = cos t, y = sin t, 0≤ ≤ 2π

II. 

III. 

IV. 

(I) and (IV)

6. 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.


7. 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


8. Which parameterization produces the ray shown below?

x = -2 + 2t, y = -3 + 3t, t≥ 0


9. 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 ≤ 2π


10. Parameterize the line segment between the points (2,4) and (5,8).x = 2 + 5t, y = 4 + 8t, 0≤ t ≤ 1



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