Does the equation x2+y=16 define y as a function of x?
No, it does not. This equation is not in the form of y = f(x), which is the form of an equation that defines y as a function of x.
stop repeating the same damn questions, willya?
To determine if the equation x^2 + y = 16 defines y as a function of x, we need to check if each value of x maps to a unique value of y.
In this equation, x^2 + y = 16, we can isolate y by subtracting x^2 from both sides of the equation:
y = 16 - x^2
Since this equation defines y as a function of x, where for every value of x, there exists a unique value of y, we can conclude that the equation x^2 + y = 16 does define y as a function of x.
To determine whether the equation x^2 + y = 16 defines y as a function of x, we need to check if the equation satisfies the vertical line test.
The vertical line test states that if every vertical line intersects the curve defined by the equation at most once, then the equation represents y as a function of x.
In this case, rearranging the equation x^2 + y = 16 gives us y = 16 - x^2.
To apply the vertical line test, imagine drawing vertical lines anywhere on the coordinate plane. If these lines intersect the graph of y = 16 - x^2 at most once, then y is a function of x.
In this case, the graph of y = 16 - x^2 will be a downward-opening parabola symmetric about the y-axis. It means that for every x-coordinate, there will be only one corresponding y-coordinate.
Therefore, the equation x^2 + y = 16 does define y as a function of x.
To solve for specific points (x, y) that satisfy this equation or to graph it, you can use various methods such as substitution, the quadratic formula, or plotting points.