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.