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Question 669648: Which of these defines a function?
1. x^2+y^2=49
2. x=|y|
3. y=[x]
4. x=y^2/8
Answer by DrBeeee(684)   (Show Source):
You can put this solution on YOUR website! The definition of a function is that for every value of the independent variable, usually x, there is one and only one (called unique) value for the dependent variable, usually y. For example
(1) y = x^2 -2x +3 is a function,
(2) y = f(x) because for any value you pick for x there is a unique value of y.
However if you have
(3) y = sqrt(x) this is not a function because y is not a single unique value for each value of x. For example, when x =4 we have
(4) y = sqrt(4) or
(5) y = +2 or -2.
Now apply the definition to your equations.
1) x^2 + y^2 = 49. We can rewrite to
(6) y = sqrt(49 - x^2) and for the same reason (4) is not a function, neither is 1). In fact, this is the equation of a circle, wherein each value of x gives two values of y.
2) x = |y|
Again, for each value of x>0, we have two values of y. Not unique, hence not a function.
3) y = [x], I don't know what this symbol means, so you're on your own here.
4) x = y^(2/8) or
(7) y = x^4, which is a function because for every value of x, you get a single, unique value for y.
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