# Points, Vectors, and Functions

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

Think you’ve got your head wrapped around

*? Put your knowledge to the test. Good luck — the Stickman is counting on you!***Points, Vectors, and Functions**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*= 2

*t*,

*y*=

*t*

^{2}

*x*=

*t*

^{2},

*y*= 2

*t*

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*= 2*t*^{2 }and*y*=*t*^{2}/2 for -4 ≤*t*≤ 4.Q. Consider the following parameterizations.

I.

x= cost, y = sint, 0≤t≤ 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 + 6

*t*,

*y*= 2

*t*

*x*= -6

*t*,

*y*= 2-2

*t*

*x*= -6 + 2

*t*,

*y*= 2 + 6

*t*

Q. Which parameterization produces the ray shown below?

*x*= -2 + 2

*t*,

*y*= -3 + 3

*t*

*x*= 2-2

*t*,

*y*= 3-3

*t*

*x*= -2 + 2

*t*,

*y*= -3 + 3

*t*,

*t*≥ 0

*x*= 2-2

*t*,

*y*= 3-3

*t*,

*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*≤ π0≤

*t*≤ 2πQ. Parameterize the line segment between the points (2,4) and (5,8).

*x*= 2 + 5

*t*,

*y*= 4 + 8

*t*, 0≤

*t*≤ 1

*x*= 5-2

*t*,

*y*= 8-4

*t*, 0≤

*t*≤ 1

*x*= 5-3

*t*,

*y*= 8 + 4

*t*, 0≤

*t*≤ 1

*x*= 2 + 3

*t*,

*y*= 4 + 4

*t*, 0≤

*t*≤ 1