# Thread: Determining if Y is a Fuction of X in an Equation

1. ## Determining if Y is a Fuction of X in an Equation

How can one determine without graphing if an equation represents y as a function of x. For example what would make {16x^2-y^2=0} not a function? And yet {y=sqrt(1-x)} a function. How is this determined?

Are there varieties of ways of determining weather an equation is a function depending what the equation consists of? Whether the equation consists of absolute values, square roots, rational expressions or combinations? Would there be different methods or formulas for determining this based on what the equation consists of? I hope my question is clear, thank you.

2. There is a formal definition of a function, but it's much easier to use something called the vertical line test. If you graph your expression and you can always make a vertical line that only touches one point, it's a function.

Put another way, given any value of x, there must only be one f(x) or y that goes along with it. If there is there is more than one (like having the points (2,1) and (2,5) ) then it's not a function.

$y=\sqrt{x}$ is only the top half of a side ways parabola. It's a function. But if you include the other half it isn't a function.

The best way to get a sense of this is to be familiar with lots of graphs and how they are formed. A lot of terms and exponents will generally be less likely to be a function.

3. Are there other threads that pretty much ask the same question. Maybe I missed them and if you can link them for me then I'll be able to feed off of these. Thanks Jameson.