You can put this solution on YOUR website! x is the independent variable
y is the dependent variable.
for every value of x, there is one and only 1 value of y.
y = x^2 would be a function
graph of that looks like this:
you can see that for each value of x there is one and only one value of y .
y^2 = x would be a relation.
solve for y to get y = +/- sqrt(x).
if any one value of x results in more than one value of y, the equation is a relation rather than a function.
in this particular case, almost every value of x results in more than one value of y as shown in the graph below:
you can see that at x = 0, there is only one value of y which is also 0.
for every other value of x for which there is a corresponding value of y, you can see that there are 2 values of y.
that makes the equation of y = +/- sqrt(x) a relation rather than a function.
that's the difference between a relation and a function.
the function has one and only one value of y for each value of x.
the relation can have more than one value of y for any value of x that that creates a value of y.
this assume x is in the domain and y is in the range.
you give the equation the vertical line test.
if only one value y intersects with the vertical line, then you have a function.
if more than one value of y intersect with the vertical line, then you have a relation.
the vertical line test has to be done for every value of x in the domain.
