Which of the following is a function?A. y squared plus 17 equals 3 x squaredB. 9 x minus 5 y squared equals 2C. 8 x cubed plus 4 y equals 32D. 9 x to the power of 4 plus 12 y squared equals 8 x squared minus 10

In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output.

Let's analyze each of the given options:

A. y squared plus 17 equals 3 x squared This is not a function because it does not pass the vertical line test. This means that there are multiple outputs (y-values) for a single input (x-value).

B. 9 x minus 5 y squared equals 2 This is not a function because it does not pass the vertical line test. This means that there are multiple outputs (y-values) for a single input (x-value).

C. 8 x cubed plus 4 y equals 32 This can be rearranged to y = -2x^3 + 8, which is a function because it passes the vertical line test. This means that there is only one output (y-value) for each input (x-value).

D. 9 x to the power of 4 plus 12 y squared equals 8 x squared minus 10 This is not a function because it does not pass the vertical line test. This means that there are multiple outputs (y-values) for a single input (x-value).

So, the only function among the given options is C. 8 x cubed plus 4 y equals 32.