Domain and range question? (1 Viewer)

[Annihilist]

Not sure how to do this. I got -5 < x < 5 for domain, not sure if that's right.

Any help is appreciated.

 

[ThandraCityRail]

you're right

25-x^2 >= 0

x^2-25<=0
(x+5)(x-5)<=0

-5<=x<=5

 

[Annihilist]

What about the range? My first instinct is to say "all real Y" but that doesn't seem right. It looks like a circle or an ellipse maybe but I have no idea, and I'm not sure how to find out the range.

 

[AAEldar]

It's the equation of the top half of an ellipse.

Think about it, the smallest value you can get on the right hand side is when , and the corresponding y value is 0. The largest value occurs when x=0 which is y=10. So the range is therefore .

Does that make sense?

 

[Annihilist]

Yes it does, thank you. I haven't done anything on ellipses yet.

 

[Carrotsticks]

Yes it does, thank you. I haven't done anything on ellipses yet.

You probably already know that the equation:



Is a semi-circle (top half specifically). The domain is x between plus/minus 5 and the range is y between 0 and 5.

Think about it this way.... the 2 at the front 'drags' the top of the semicircle up by a scale of 2, so instead of being between 0 and 5, it is now between 0 and 10.

So if I had 3 at the front, the range would be from 0 to 15. If I had a 0.5 at the front, the range would be from 0 to 2.5 etc etc.

Here is a picture of the semicircle and the new curve so you can see the 'dragging' effect.

 

[SpiralFlex]

An alternative (scroll down to my post ages ago...)

http://community.boredofstudies.org/showthread.php?t=266737

 

[Annihilist]

You probably already know that the equation:



Is a semi-circle (top half specifically). The domain is x between plus/minus 5 and the range is y between 0 and 5.

Think about it this way.... the 2 at the front 'drags' the top of the semicircle up by a scale of 2, so instead of being between 0 and 5, it is now between 0 and 10.

So if I had 3 at the front, the range would be from 0 to 15. If I had a 0.5 at the front, the range would be from 0 to 2.5 etc etc.

Here is a picture of the semicircle and the new curve so you can see the 'dragging' effect.

Makes sense. Thank you.