Yes, \( y = 2x^3 \) is a function. A function is defined as a relation in which each input (or independent variable, in this case \( x \)) has exactly one output (or dependent variable, in this case \( y \)).
In the equation \( y = 2x^3 \), for every value of \( x \), there is a unique value of \( y \). Specifically, the term \( 2x^3 \) will produce a single output for each input value of \( x \). Therefore, \( y = 2x^3 \) meets the criteria of a function.
You can also verify that this is a function by checking that it passes the vertical line test, which states that if a vertical line intersects the graph of the relation at more than one point, then it is not a function. However, since \( y = 2x^3 \) is a polynomial, it will pass the vertical line test.
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