evaluate function f(x) = 3x-6 , f(1/3x) and f(x)/3

Let's evaluate the function \( f(x) = 3x - 6 \) for \( f\left(\frac{1}{3}x\right) \) and \( \frac{f(x)}{3} \).

### 1. Evaluate \( f\left(\frac{1}{3}x\right) \):

We substitute \( \frac{1}{3}x \) into the function \( f(x) = 3x - 6 \).

\[
f\left(\frac{1}{3}x\right) = 3\left(\frac{1}{3}x\right) - 6
\]

Simplifying:

\[
f\left(\frac{1}{3}x\right) = x - 6
\]

### 2. Evaluate \( \frac{f(x)}{3} \):

We take the expression for \( f(x) = 3x - 6 \) and divide it by 3.

\[
\frac{f(x)}{3} = \frac{3x - 6}{3}
\]

Simplifying:

\[
\frac{f(x)}{3} = x - 2
\]

### Summary of Results:
- \( f\left(\frac{1}{3}x\right) = x - 6 \)
- \( \frac{f(x)}{3} = x - 2 \)

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Would you like more details or have any questions?

Here are 8 related questions you might find helpful:

1. How do you evaluate a function for a specific input value?
2. What does it mean to compose functions, and how does it differ from evaluating them?
3. Can you find the inverse of the function \( f(x) = 3x - 6 \)?
4. What is the domain and range of the function \( f(x) = 3x - 6 \)?
5. How do you graph the function \( f(x) = 3x - 6 \) on a coordinate plane?
6. What happens to the graph of a function when you multiply it by a constant?
7. How do you find the x-intercept and y-intercept of the function \( f(x) = 3x - 6 \)?
8. What are the effects of horizontal and vertical translations on the graph of a function?

**Tip:** Always substitute carefully and simplify step by step to avoid errors in function evaluation.

Learn how to evaluate the function f(x) = 3x - 6 for specific inputs and its variants like f(1/3x) and f(x)/3. This problem covers key concepts in function evaluation, linear functions, and division of functions. Suitable for Grades 7-9.

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