Find an expression for the for the function whose graph is the given curve. Give the domain and range.

The bottom half of the circle whose center is @(3,0) and has a radius of length 5.

I'm so lost.

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- Jun 7th 2010, 11:58 AMtigergirlEquation of a half circle
Find an expression for the for the function whose graph is the given curve. Give the domain and range.

The bottom half of the circle whose center is @(3,0) and has a radius of length 5.

I'm so lost. - Jun 7th 2010, 12:29 PMp0oint
Here is the equation of the whole circle.

$\displaystyle (x-3)^2+y^2=5^2$

Now find y1 and y2, the negative square root would be the botom half of the circle.

Regards. - Jun 7th 2010, 12:32 PMSpringFan25
Lets find the equation of the full circle first.

This is $\displaystyle y^2 + (x-3)^2 = 5^2$

Rearrange for Y

This is $\displaystyle y = \sqrt{25 - (x-3)^2}$

When it is in this form, the range and domain are defined as follows:

The**domain**is all possible values that x can take

The**range**is all possible values that y can take

Because it is a circle with radius 5, centered around (3,0); you know the domain and range are:

Domain: $\displaystyle -2 \leq x \leq 8 $

Range: $\displaystyle -5 \leq y \leq 5 $

You want the**bottom half**of the circle, which is the part where Y<0.

Hopefully, you can see that

Domain: $\displaystyle -2 \leq x \leq 8 $ (the same)

Range: $\displaystyle -5 \leq y \leq 0 $ (bottom half only)

This is much easier to draw than do in your head. I'll try to attach an image later

**edit**too slow - Jun 8th 2010, 06:33 PMAltermeris
I got the same answer as

*SpringFan25.*(Nod)