testing for functions represented algebraically??

Question

I can't figure out how to solve these

determine whether equations represents a function and show work.

1.  x² + y² = 4 
2.  2x + 3y = 4
3.  (x-2)² + y² = 4
4.  y= √x+5

Answer 1

Solve each equation for y. If for any x-value you get back more than one y-value, then it is not a function of y.

x^2 + y^2 =4. So y^2 = 4-x^2. Take square root of both sides.

So y= +/-sqrt (4-x^2). This is not a function since you can get back two y-values for some x-values. For example if x=1, then y=+/-sqrt(4-1^2)= +/- sqrt(3) which is two values.