Find the domain and the range of the relation shown on the graph to the right. Use the vertical line test to determine whether
the graph is the graph of a function.

Domain = {0.-6}

Range = {-2, 4}  

Notes We find coordinates and radius and state

Then we show formula  (x -x1)^2 + (y +y1) = r ^2 and show

(x -3 )^2 + (y − 1)^2 = 9 = R^2  THE RADIUS^2

then ;

Domain formula = x - r   and x + r

Range formula = y - r  and  y + r

Step-by-step explanation:

The graph is a circle so all the points are enclosed in it

The domain is the values for x so you subtract the radius from the centre coordinate and you add the radius to it The range is the values for y so you do the same to the y coordinate If you use

(x- x1) ^2 + (y - y1) ^2

(x -3 )^2 + (y − 1)^2 = 9

However this changes if centre coordinate shows negatives

we change negative x or y to + positive in the formula in bold.

Centre coordinate = (3.,1) radius is 3  SO = MUST BE THE RADIUS ^2

= (x - 3)^2 + (y - 1)^2 = 3^2  = 9  

Domain formula = x - r   and x + r

Domain  = 3 - 3 = 0

and - 3 + 3 = -6

Domain = {0.-6}

Range formula = y - r  and  y + r

Range = 1 - 3 = -2

and  1 +3 = 4

Range = {-2, 4}  

because linear equations are a lot simpler than quadratics equations, and linear equations formula is a lot easier to memorize. that's why i think they're harder.