To determine whether the relation \( y = 2x^3 \) is a function, we need to check if each input \( x \) corresponds to exactly one output \( y \).
In this case, for every value of \( x \), the expression \( 2x^3 \) provides a unique value of \( y \). No \( x \) value will result in more than one \( y \) value, which satisfies the definition of a function.
As for identifying functions from tables, if you have a set of input-output pairs, you would check to ensure that no two different inputs (x-values) have the same output (y-value). If they do, that relation would not be a function.
If you have specific tables or relations to discuss, please provide that information for further analysis!