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### Given:
The function \( f(x) = \frac{1}{3}x \).

#### Part (a): Evaluate \( f(-2) \) and \( f(4) \)
To solve this, we substitute \( x = -2 \) and \( x = 4 \) into the function \( f(x) = \frac{1}{3}x \).

- \( f(-2) = \frac{1}{3}(-2) = -\frac{2}{3} \)
- \( f(4) = \frac{1}{3}(4) = \frac{4}{3} \)

So:
- \( f(-2) = -\frac{2}{3} \)
- \( f(4) = \frac{4}{3} \)

#### Part (b): Graph \( f(x) \). How can the graph of \( f \) be used to determine the zero of \( f \)?
The graph of \( f(x) = \frac{1}{3}x \) is a straight line passing through the origin with a slope of \( \frac{1}{3} \). The zero of a function is the point where the graph intersects the x-axis, which occurs when \( f(x) = 0 \).

#### Part (c): Find the zero of \( f \)
To find the zero, we set \( f(x) = 0 \) and solve for \( x \):

\[
\frac{1}{3}x = 0
\]

Multiplying both sides by 3, we get \( x = 0 \).

So, the zero of \( f(x) \) is at \( x = 0 \).

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Would you like a detailed graph or further clarification on any part of this solution? Here are some additional questions to deepen your understanding:

1. How would the graph of \( f(x) = \frac{1}{3}x \) compare to that of \( f(x) = \frac{1}{2}x \)?
2. What does the slope \( \frac{1}{3} \) represent in the context of the function \( f(x) = \frac{1}{3}x \)?
3. Can a linear function like \( f(x) = \frac{1}{3}x \) have more than one zero?
4. How does changing the slope in a linear function affect the position of the zero?
5. How would you verify graphically that the zero of the function is \( x = 0 \)?

**Tip**: When determining the zero of a linear function, always look for where the graph crosses the x-axis, as this represents the value of \( x \) where \( f(x) = 0 \).

For the linear function f(x) = 1/3 * x, evaluate f(-2) and f(4). Graph f. How can the graph of f be used to determine the zero of f? Find the zero of f.

Learn how to evaluate the linear function f(x) = (1/3) * x at given points and determine its zero. Understand how to graph the function and use it to find where it crosses the x-axis. This problem covers key concepts related to linear functions and graphing. Suitable for students in Grades 6-8.

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