By: Stephen Bismarck
Explore x = t+1 , y = 2t-1
If this parametric equation is graphed
from [0,10] for t the graph looks like this
It looks like a line segment
If the range is increased to [-10,10],
what happens to the graph?
The line segment is bigger, including
more negative values, but not a complete line.
How could we make this a line?
We could make the range from but we can't graph infinity
We can replace the infinities with
a really big number like 5,000,000 and see what happens
It looks like this is a complete line,
but if the screen is expanded you'll see it is only a segment
If we solve for t in both of the equations
let's see what we get
t = x-1 and t =1/2 (y+1)
x-1 = 1/2 (y+1)
2x -2 = y+1
y = 2x -3
As you can see some parametric equations
are only peices of a function