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The question asks how to reflect the function \( f(x) = \frac{2}{3}x - 9 \) over the **y-axis**.

When a function is reflected over the **y-axis**, we replace \( x \) with \( -x \) in the function. So, let's reflect the function step by step:

1. Start with the original function:
   \[
   f(x) = \frac{2}{3}x - 9
   \]

2. To reflect over the y-axis, replace \( x \) with \( -x \):
   \[
   g(x) = \frac{2}{3}(-x) - 9
   \]

3. Simplify:
   \[
   g(x) = -\frac{2}{3}x - 9
   \]

Thus, the reflected function is:
\[
g(x) = -\frac{2}{3}x - 9
\]

This corresponds to the third option in your quiz: **g(x) = -\(\frac{2}{3}x - 9\)**.

Let me know if you want any further details!

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Here are five follow-up questions related to this concept:
1. How does reflecting a function over the x-axis differ from reflecting over the y-axis?
2. What happens to the slope when a linear function is reflected over the y-axis?
3. If \( f(x) = ax + b \), what will the reflected function over the y-axis be in general terms?
4. How would you reflect a quadratic function over the y-axis?
5. Can a function remain unchanged when reflected over the y-axis? If so, what type of function?

**Tip:** To reflect a function over the y-axis, simply replace \( x \) with \( -x \) in the function equation!

With the parent function being f(x) = 2/3x - 9, how would you write the function when reflected over the y-axis?

Learn how to reflect the linear function f(x) = 2/3x - 9 over the y-axis. This guide covers key algebraic concepts, including function transformations and reflection rules, suitable for students in Grades 8-10.

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