For each of the following, determine whether the equation defines y as a function of x.

Question

Y=2|x|-5

x=y^2÷3

(y+3)^2-9=x

6x+|y|=0

Answer 1

Y=2|x|-5 is the only function. Each of the others are relations and not functions. Each of the other relationships can have two different y values for the same x which would contradict the definition of a function

Answer 2

yes

no

no

no

the NO's win, 3 to 1

1st is the only function

the last 3 are not functions as they fail the vertical line tes

the last 3 have more than one y value for a given x value

they have 2 outputs for just one input

while the 1st is a function, it's not a one to one function as it fails the horizontal line test

IF y shows up with a 2 or even numbered exponent or inside an absolute value sign, with the expression =x then it's not a function.

just try out a few y values, such as 1 and -1, they both give the same x value. That's 2 y's for one x. You can't tell what the y value is if all you know is the x value. That disqualifies it as a function. Just by definition.

x= (y^2)/3

x = ((-1)^2)/3 = 1/3

but so does ((+1)^2)/3 = 1/3

one x value leaves y indeterminate