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.
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