Final answer:
To find y at the point (1,-1), if the function is odd as suggested by y(x) = -y(-x), we would expect y at x=1 to be the opposite of y at x=-1. However, additional information about the function's explicit form is needed to make precise calculations.
Step-by-step explanation:
If the function implicitly defines y as a function of x, and we want to determine the value of y at the point (1,-1), we need to consider the given relationship y(x) = −y(−x). This relationship suggests the function has symmetry, similar to even and odd functions. An even function is symmetric about the y-axis, and an odd function (anti-symmetric function) is symmetric about both axes.
To find y at the point (1,-1), we first note that if y(x) is equal to minus y(-x), it indicates that we have an odd function.
So, if we plug x=1 into the function, we find that y(1) would be -y(-1).
Given that the point (1,-1) lies on the function, we would then have y(1) = -(-1) = 1.
However, since the student is asking what y is at (1,-1), we could say that the function prescribes y to be -1 at x=1. It's important to remember that the function needs to be explicitly given to precisely determine the value of y based on the value of x. Without the function's form, we can't perform direct calculations, but we can analyze what's provided for general insights about the function's behavior.