Question

define whether each equation defines Y as a function of X ( X+Y^2=5)

Answer 1

Not a function in x, since if you solve for y it becomes clear that one x would be paired with twp y-values (violates definition)\[x+y^2=5\]\[y^2=5-x\]\[y=\pm \sqrt{x-5}\]

Answer 2

Ex. let x=9, then\[y=\pm \sqrt{9-5}=\pm \sqrt{4}=\pm 2\]
Thus (9,-2) and (9,2)

Answer 3

If it were a function in x, then each x-value would be paired with one and only one y-value

Answer 4

so it cant be squared
what if the question is X^2 +Y =5

Answer 5

THAT IS A FUNCTION RIGHT

Answer 6

That is ok since you would have\[y=-x^2+5\]each x would pair with only one y-value (not uniquely) but with only one at a time

Answer 7

right it is a function in x

Answer 8

THANKS

Answer 9

ur welcome :})