Equations Given A Function?

Question

Determine if each equation given is a function. If it is or is not a function, explain the reason why. How do I know if an equation is a function or not?

(1) y = + or - sqrt{1 - 2x}

(2) y = (3x - 1)/(x + 2)

Answer 1

(1) y = + or - sqrt{1 - 2x}

are the { } suppose to be absolute value?
If so then it isn't a function because for every y values their is more than one possible x.

The definition of function is that for every given x their is exactly one y value.

If those are just suppose to be ( ) then it is a function because for every given x their is exactly one y value.

(2) y = (3x - 1)/(x + 2)
It is a function because for every given x their is exactly one y value even though when x=2 the y value DNE.

Answer 2

(1) y = + or - sqrt{1 - 2x}
Not a function since a single value of x can produce two different values of y.

(2) y = (3x - 1)/(x + 2)
This is a function which is discontinuous at x = -2
There is a single value of y produced by eac value of x except when x = -2 at which time y is undefined.

The 1st equation does not pass vertical linne test. The 2nd equation does.

Answer 3

(1) not a function, since for each x value, you have two y values.
(2) yes.