We are given the function:

$f(x) = 4 \left| 3x - 1 \right|$

Now, let's evaluate the function at the given values.

1. $f(-3)$

$f(-3) = 4 \left| 3(-3) - 1 \right| = 4 \left| -9 - 1 \right| = 4 \left| -10 \right| = 4(10) = 40$

2. $f(2)$

$f(2) = 4 \left| 3(2) - 1 \right| = 4 \left| 6 - 1 \right| = 4 \left| 5 \right| = 4(5) = 20$

3. $f(-a)$

$f(-a) = 4 \left| 3(-a) - 1 \right| = 4 \left| -3a - 1 \right| = 4 \left| -(3a + 1) \right| = 4(3a + 1)$ (Since the absolute value of a negative expression is the same as the positive counterpart.)

4. $-f(a)$

$-f(a) = -\left( 4 \left| 3a - 1 \right| \right) = -4 \left| 3a - 1 \right|$

5. $f(a + h)$

$f(a + h) = 4 \left| 3(a + h) - 1 \right| = 4 \left| 3a + 3h - 1 \right|$

Let me know if you want further clarification or details on any of the steps!

---

Here are 5 related questions to extend this topic:

1. What happens to $f(x)$ as $x \to \infty$?
2. How does the function $f(x)$ change if we replace $| \cdot |$ with $\cdot$?
3. What is the minimum value of $f(x)$?
4. How would you find the inverse of the function $f(x)$?
5. How does the function behave when $x$ is negative compared to when $x$ is positive?

Tip: When dealing with absolute value functions, always consider breaking the expression into cases based on where the expression inside the absolute value becomes positive or negative.