reflection of a function over the x-axis

1. Understand the transformation: The problem asks for the table representing $y = -f(x)$. A negative sign in front of the function $f(x)$ indicates a reflection of the graph over the $x$-axis. This transformation changes the sign of the $y$-coordinates while keeping the $x$-coordinates the same. If a point on the original graph is $(x, y)$, the corresponding point on the reflected graph will be $(x, -y)$.

1. Identify points on the original graph: From the provided graph, we can identify three specific points: $(2, 0)$, $(3, 1)$, and $(6, 2)$. These represent the values of $f(x)$ for $x = 2, 3, 6$.

3. Calculate the reflected values: To find the values for $-f(x)$, we negate the $y$-coordinates of the points identified in step 2:
- For $x = 2$, $f(2) = 0$, so $-f(2) = -0 = 0$.
- For $x = 3$, $f(3) = 1$, so $-f(3) = -1$.
- For $x = 6$, $f(6) = 2$, so $-f(6) = -2$.

4. Compare with the given options: We are looking for a table that contains the pairs $(2, 0)$, $(3, -1)$, and $(6, -2)$. Looking at the choices provided, the last table matches these values exactly:
- $x=2, -f(x)=0$
- $x=3, -f(x)=-1$
- $x=6, -f(x)=-2$