Determine whether the equations define y as a function of x

Question

Determine whether the equations define y as a function of x.

y=x^2-4

Answer 1

Yes.

If y = x² - 4, then y is a function of x.

In this case, y is the dependent variable of the function and x is the independent variable of the function.

Why is this true?

Because the value of y is dependent upon the value that is plugged in for x, but the value of x is not dependent upon the value that is plugged in for y.

You can also tell this is a function because for any value of x you use in this function, there will be exactly one y value corresponding to that value of x. No more than one y value, and no less than one y value.

You can also tell that y is a function of x by plotting y = x² - 4 in a graphing calculator and using the vertical line test to determine that y is indeed a function of x.

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