input 2 4 3 2 output 20 40 30 40 Determine whether each relation is a function.(4 points)

Question

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y=2x3y=2x3
Function
Not a Function
Function

Answer 1

To determine if the relation $y=2x^3$ is a function, we need to remember that a relation is a function if every input corresponds to exactly one output.

Given the equation $y=2x^3$, for every value of $x$ there is a unique value of $y$. For example:

• If $x=2$, then $y=2(2^3)=2(8)=16$.
• If $x=4$, then $y=2(4^3)=2(64)=128$.
• If $x=3$, then $y=2(3^3)=2(27)=54$.
• If $x=2$ (again), $y=16$ (as calculated before).

Since for every input $x$ there is only one corresponding output $y$, the relation is indeed a function.

So the answer is: Function.