horizontal reflection of cubic function

1. Understand the transformation: A horizontal reflection of a function $f(x)$ across the y-axis is represented by the function $f(-x)$. Given $f(x) = x^3$, the reflected function is $f(-x) = (-x)^3$.

1. Simplify the expression: Using the properties of exponents, $(-x)^3 = (-1)^3 \cdot x^3 = -x^3$. Therefore, to find the values for the table, we need to calculate $-x^3$ for each given $x$.

3. Calculate the values:
- For $x = 0$: $f(-0) = -(0)^3 = 0$.
- For $x = 1$: $f(-1) = -(1)^3 = -1$.
- For $x = 2$: $f(-2) = -(2)^3 = -8$.

4. Final Table:
- When $x = 0$, $f(-x) = 0$.
- When $x = 1$, $f(-x) = -1$.
- When $x = 2$, $f(-x) = -8$.