00:01
So in this question, we are given two curves, f and g.
00:09
And we are told that they represent a parametric equation.
00:15
So a path, really, f of the g of t, and we're asked to find or draw this graph.
00:25
So for this question, there is like two ways we can go about this.
00:30
We can try to find the formulas or else.
00:32
F and g and then it's the standard question.
00:37
Like you've given x and y, and then you figure it out from there.
00:47
You isolate and sub in and everything.
00:51
We can also do it slightly differently.
00:54
So we know a couple of points.
01:01
We can tell that f is a linear function.
01:06
So we can sort of guess that minus one, it's going to be two.
01:11
So now we have three points on our curve.
01:16
So let's draw our curve down here.
01:20
So we have t equals minus one, t equals zero, t equals one.
01:27
And then we are going to estimate like what happens at minus infinity and what happens at plus infinity.
01:38
Okay, so for t is minus one, x is two, and y is zero.
01:46
We can just read that off from the graph for t here.
01:50
For t is zero, we know from the graph, x equals 1, as does y.
01:56
For t equals 1, we get x equals 0 and y equals 0 as well.
02:07
So at negative infinity, x is going to be, we can't quite tell if this is actually a linear function.
02:16
Because we're just given the graph.
02:17
We don't actually know what happens, but we'd expect this to be roughly infinity.
02:25
Sorry, not minus infinity, just infinity.
02:28
Well, why would be roughly, let's say minus infinity square.
02:33
It looks like a parabola.
02:37
And minus infinity squared, these are not actually equations.
02:43
They're just kind of notes for you and me to say, well, x becomes infinity and y becomes minus infinity, but y becomes infinity faster...