Given the function:
![y-3x^3=2](https://img.qammunity.org/2023/formulas/mathematics/college/6sopsqhyol1xay4javy8il7izu1aybv5gj.png)
Clearing y:
![y=3x^3+2](https://img.qammunity.org/2023/formulas/mathematics/college/u5rabhk2gc46k26p9hwk0b4kwfs00huj9v.png)
And now, we are going to analyze the domain of the function:
As you can see, the function is a polynomial. In this case the function will exist at all values of x.
that is, there will always be an image in y for each value of x.
Therefore, the equation is a function.