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The given function \( f(x) \) is a piecewise function defined as follows:

\[
f(x) = 
\begin{cases} 
2x - 6 & \text{if } x \leq 3 \\
x^2 - 9 & \text{if } x > 3
\end{cases}
\]

Let me know if you'd like me to analyze a specific aspect of this function, such as determining its continuity at \( x = 3 \), differentiability, or behavior for specific values.

Would you like me to explore any particular property of this function? Here are a few suggestions:

1. Calculate the value of \( f(x) \) at specific points like \( x = 3 \), \( x = 0 \), and \( x = 4 \).
2. Determine if the function is continuous at \( x = 3 \).
3. Find the derivative of each part of the function.
4. Analyze the limits of the function as \( x \) approaches 3 from both sides.
5. Graph the function to visualize its behavior.

**Tip:** For piecewise functions, always check for continuity and differentiability at the points where the function changes definition.

Given function f(x) is a piecewise function defined as follows:
 f(x) = 2x - 6 if x <= 3 
 f(x) = x^2 - 9 if x > 3

Explore the behavior of the piecewise function defined by f(x) = 2x - 6 for x <= 3 and f(x) = x^2 - 9 for x > 3. This problem involves concepts such as continuity, limits, and the behavior of linear and quadratic functions. Suitable for Grade 10 students.

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