Does the equation x^2+y=16 define y as a function of x?
Yes, the equation x^2+y=16 defines y as a function of x.
stop repeating the same damn questions, willya?
To determine if the equation defines y as a function of x, we need to check if for every value of x, there is a unique value of y.
In the equation x^2 + y = 16, we can rewrite it as y = 16 - x^2.
Since x^2 is a polynomial function of x, it is continuous and defined for all real numbers.
Therefore, for every value of x, we can find a corresponding unique value of y by plugging in that value of x into the equation y = 16 - x^2.
Hence, the equation y = 16 - x^2 defines y as a function of x.
To determine if the equation defines y as a function of x, we need to check if for each value of x, there is only one corresponding value of y.
In the given equation, we have x^2 + y = 16. To express y as a function of x, we need to isolate y on one side of the equation.
Rearranging the equation, we get y = 16 - x^2.
Since for each value of x, there is only one corresponding value of y, we can conclude that the equation y = 16 - x^2 defines y as a function of x.