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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 ≤ tM 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, -1)

4. Determine which picture best represents the graph of the parametric equations x = 2t2 and y = t2/2  for -4 ≤ t ≤ 4. ->
5. Which of the following options are parametrizations of the unit circle?

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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