Question

Determine whether the equation defines y as a function of $x$.

$y=x^3$

Short answer

The given equation is a function.

Step-by-step solution

Step 1. Given information

In the given question we have to determine whether the equation defines y as a function of x.

$y=x^3$

Step 2. The given equation is y=x3

The equation tells us to take an input $x$and find their square.

For any input $x$, these operations yield only one output $y$.

Step 3. For example, 

If $x=1$, then $y={\left(1\right)}^3=1$.

If $x=1$, then $y={\left(2\right)}^3=8$.

For this reason, the equation is a function.