Find the values for the function f(x) 3 multiplied by the absolute value of (3x-2) the with transformations of f(a+h); -f(a), f(-a)

We are given a function \( f(x) = 3|3x - 2| \), and we are asked to find the values of the function under the following transformations: \( f(a+h) \), \( -f(a) \), and \( f(-a) \).

### 1. \( f(a+h) \)

For this transformation, substitute \( a+h \) into the original function in place of \( x \):

\[
f(a+h) = 3|3(a+h) - 2|
\]

Now simplify the expression:

\[
f(a+h) = 3|3a + 3h - 2|
\]

### 2. \( -f(a) \)

For this transformation, we take the negative of \( f(a) \). Start by substituting \( a \) into the original function:

\[
f(a) = 3|3a - 2|
\]

Then, apply the negative:

\[
-f(a) = -3|3a - 2|
\]

### 3. \( f(-a) \)

For this transformation, substitute \( -a \) into the original function in place of \( x \):

\[
f(-a) = 3|3(-a) - 2|


Find the values for the function f(x) = 3 multiplied by the absolute value of (3x-2) with transformations of f(a+h), -f(a), f(-a)

Explore the transformations of the absolute value function f(x) = 3|3x - 2|, including f(a+h), -f(a), and f(-a). This solution covers algebraic concepts like function transformations, absolute value functions, and step-by-step calculations. Suitable for students in Grades 9-11.

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