**Problem : **
Is the following plane curve a function: *y* = 3*t*^{2}, *x* = , 0≤*t*≤5?

Yes. By examining the graph, you can see that for every

*x*, there is only one

*f* (*x*).

**Problem : **
The following plane curve is a circle: *x* = 2 cos(*t*), *y* = 2 sin(*t*), 0≤*t* < 2*Π*. Is its orientation clockwise or couterclockwise? What happens
when you reverse the parametric equations, so that *x* = 2 sin(*t*), *y* = 2 cos(*t*)?

The orientation of the first curve is counterclockwise. When the functions for

*x* and

*y* are exchanged, the curve's orientation becomes clockwise.

**Problem : **
Convert the parametric equation *x* = 2*t*, *y* = , *t* > 0, to a
rectangular equation.

*y* = .

**Problem : **
How many times does the graph of *x* = *t*^{2} - *t* - 6, *y* = 2*t*, -5 < *t* < 5 cross
the *y*-axis?

Twice, when

*t* = - 2 at

(0, - 4) and when

*t* = 3 at

(0, 6).

**Problem : **
Jim and Bob are racing from the origin to the point (5, 10). Let *t* be the
number of seconds after the start of the race. Jim's position at any time *t*
is given by the parametric equations *x* = *t*, *y* = 2*t*. Bob's position at any
time *t* is given by the parametric equations *x* = 5*t*, *y* = 10*t*. Who will win
the race? How long does it take each competitor to finish the race?

Jim reaches the point

(5, 10) after

*t* = 5 seconds. Bob will reach the point

(5, 10) after

*t* = 1 second. Bob will win the race.