Questions: Which of the following relations represent (y) as a function of (x) ? Select all that apply. (5x+2y^3=-3) None of the above

Solution Steps

The equation \(5x + 2y^3 = -3\) can be rewritten to express \(y\) in terms of \(x\): \(2y^3 = -3 - 5x\) \(y^3 = \frac{-3 - 5x}{2}\) \(y = \sqrt[3]{\frac{-3 - 5x}{2}}\) For each value of \(x\), there is only one value of \(y\). Therefore, the equation \(5x + 2y^3 = -3\) represents \(y\) as a function of \(x\).

The table shows two different values of \(y\) (-3 and -2) for the same value of \(x\) (-1). Since a function must have only one output for each input, this table does not represent a function.

Final Answer