Question

determine whether the equation represents y as a function of x. x^2+y^2=4

Answer 1

No. This is a relation only.

Answer 2

nope. this is a circle with center (0,0) radius 2 to fails vertical line test

Answer 3

also notice that (0,2) and (0,-2) fits this equation, so two inputs give different outputs. says the same thing really

Answer 4

how about x+ y^2=4

Answer 5

No again. If you were to solve for y you would get\[y= \pm \sqrt{4-x}\]indicating two y-values for each choice of x

Answer 6

thank you.

Answer 7

(except x=4)

Suppose x=-5, then\[y= \pm \sqrt{4-(-5)}= \pm \sqrt{9} = \pm3\]This implies the points (-5, -3) and (-5, 3). One domain value is paired with more than one range value. Therefore not a function in x.