Question

Identify the center, domain, and range of the graph.

Can you please explain to me how to find these? @mathmale I'll put the graph in one moment.

Answer 1

Great to "see" you again on OpenStudy!!

Nicole, please refer to the graph. Can you identify the center of this ellipse?
From the center to the right vertex, how far?

Answer 2

Hello, it's nice to "see" you again to!
Center (0,0)
To the right vertex is 3?

Answer 3

Yes, the center is at (0,0). Let's use your other answer in this way: The right vertex is at (3,0). What is the left vertex? (We don't need it; this is just for practice).

Answer 4

Left vertex would be (-3,0)

Answer 5

Now suppose you travel from the center upward along the y-axis. What is the max. distance of the eliipse from the center in that direction?

Answer 6

Top - (2, 0)
Bottom - (-2, 0)

Answer 7

Can you identify the point at which you're vertically as far as you can get from the center?

Answer 8

Great. Because the ellipse is longer along the x-axis than it is wide, we say it's "horizontal."
The distance "a" is called your semi-major axis and has length 3.
The dist. " b " is called your semi-minor ax. and has length 2. OK?

Answer 9

Urge you to write this down, if you don't already have it in a reference book or online.

Answer 10

Okay, and yes I've been working with a tutor but I didn't get to work this with them so it's a bit confusing.

Answer 11

You now have the left and right vertices. How far apart are they? What is the smallest x value? What is the largest?

You also have the top and bottom "co-vertices." the variable y varies from ?? to ?? along the y-axis.

Answer 12

Left and right vertices are 6 units apart?

Answer 13

Taking your answer to the first question: Your x ranges from (and includes) x=-3 to (and including) x=3. Agreed? This is your DOMAIN.

Answer 14

Yes

Answer 15

And the range would be the same but with -2 and 2 ?
@mathmale

Answer 16

Yes. Say: Domain is ]-3,3]; Range is [-2,2]. That's it!

Answer 17

Have you studied "foci" as well?

Answer 18

Awesome! Can you help with another? I'll open a new post of course (:

Answer 19

I'll be helping a number of others simultaneously. If you understand that and are not bothered, then YES!

Answer 20

Of course not! Thank you (: