what is the domain and range for th equation in this question

what is the domain and range for the equations here? can I just substitute the range of t into x and y?
is the domain and range (-4+9the root of 3)/2<x<-2, and -7/2<y<10?

(edited 3 years ago)

Screenshot_3.png71.6KB

Reply 1

mqb2766

Original post by Hedwigeeeee

what is the domain and range for the equations here? can I just substitute the range of t into x and y?
is the domain and range (-4+9the root of 3)/2<x<-2, and -7/2<y<10?

The question doesn't ask for this? For c) its just the length of an arc.

May be wrong on this, but the domain is on t for parametric curves.

(edited 3 years ago)

Reply 2

Hedwigeeeee

Original post by mqb2766

The question doesn't ask for this? For c) its just the length of an arc.

May be wrong on this, but the domain is on t for parametric curves.

I know it does not ask, i just to want to check if my domain and range are correct.

Reply 3

mqb2766

Original post by Hedwigeeeee

I know it does not ask, i just to want to check if my domain and range are correct.

You don't really have a dependent / independent distinction for x - y curves in parametric curves. I thought that the domain was on t, not x?

Reply 4

B_9710

You only really say domain and range for functions. The curve C isn’t described by a function as it’s a circle. So it’s tough to say what you really mean when you ask for the domain and range. But if you’re asking for the values of x and y that the curve C can take, then you can’t just plug the range of t into x and y.
To see this imagine a curve given by

y=x^2, \ \ -1\leq x \leq 1

. If you plug in the range of x in you might think

-1\leq y \leq 1

. But of course it isn’t

Reply 5

B_9710

To answer the question, you have the equation of a circle. So if you draw a sketch of it, since you know it’s centre and radius you should be able to determine that min/max values that x and y can take.
You could also do it algebraically but not as easy.

Reply 6

Hedwigeeeee

Original post by B_9710

so sometimes we cannot just plug t into the equation for x and y to get domain and range, right?it depends on the drawing?

Reply 7

mqb2766

Original post by Hedwigeeeee

so sometimes we cannot just plug t into the equation for x and y to get domain and range, right?it depends on the drawing?

The domain is on t. You can talk about the ranges of the x and y variables.
https://www.youtube.com/watch?v=_PcLRVulbNA&app=desktop
Most of the time, the parametric curve is not an x-y function, so the x domain, y range does not apply.

Reply 8

B_9710

Original post by Hedwigeeeee

so sometimes we cannot just plug t into the equation for x and y to get domain and range, right?it depends on the drawing?

Yeah, and in general you can’t just plug in the range for t and expect to get the right answer. You really need to understand what you’re working out and why.
To understand range of a function, you need to be able to determine turning points, value of y as x tends to positive infinity or negative infinity. Things like that. Can be very difficult to do sometimes if the equation of a curve is complicated.