Question

How do I determine whether or not an equation is a function without graphing?

Answer 1

If every input gives one and only one unique output, it is a function.

Answer 2

Eg. That is a function.

Answer 3

That is not.

Answer 4

My bad, I meant to say without graphing. I know about the vertical line test. Could you show me some relations that that aren't functions in the form of an equation.

Answer 5

Relations that are functions can always be written in the form y=f(x)=blah blah (some function of x WITHOUT any y's)
Here are some examples of functions
y=x^3
y=x^x
y=e^x-5x+23x^(1/2)
y^3=x (in the reals, this comes down to y=x^(1/3))
Here are some examples of relations that aren't functions
y^2=x
y^2+y^3=x
x^2=y^2

Answer 6

y^2=x is not a function because it is the union of the functions y=sqrt(x) and y=-sqrt(x), The solutions for y for all of the other relations that aren't functions can similarly exist as multiple functions for a single value of x, which is why by definition they are not a function...

Answer 7

Thank you!