To complete the table, we need to evaluate $f(x) = -2|x|$ for each given $x$ value by following these steps:

1. Calculate the absolute value $|x|$.
2. Multiply the absolute value by -2 to get $f(x)$.

Let's go through each value of $x$:

1. For $x = -1$:

   • $|x| = | -1 | = 1$
   • $f(x) = -2 \times 1 = -2$

2. For $x = 0$:

   • $|x| = |0| = 0$
   • $f(x) = -2 \times 0 = 0$

3. For $x = 1$:

   • $|x| = |1| = 1$
   • $f(x) = -2 \times 1 = -2$

4. For $x = 2$:

   • $|x| = |2| = 2$
   • $f(x) = -2 \times 2 = -4$

So, the completed table should look like this:

Would you like more details or have any questions?

Here are some related questions that might help you understand the concept better:

1. How does the absolute value affect the output of the function?
2. What would happen if the coefficient was positive instead of negative?
3. How does the function behave for positive and negative values of $x$?
4. What is the general shape of the graph for $f(x) = -2|x|$?
5. How does changing the value of -2 in the function affect the table values?

Tip: Always calculate the absolute value first when working with functions involving $|x|$, as it simplifies determining the effect on the final output.