Evaluate the function *f*

at the indicated values. *f*(*x*)=4|3*x*−1| f(-3),f(2),f(-a),-f(a),f(a+h)

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!

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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.

Evaluate the function f at the indicated values. f(x) = 4|3x−1|, f(-3), f(2), f(-a), -f(a), f(a+h)

Learn how to evaluate the absolute value function f(x) = 4|3x - 1| at various values including f(-3), f(2), f(-a), -f(a), and f(a+h). This problem covers key algebraic concepts such as absolute value functions and function evaluation, suitable for students in Grades 9-11.

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