f(x) = \begin{cases}
\dfrac{5}{x} &   \text{for} ~~~~x\gt{5} \\
x-4&  \text{for} ~~~~ x \leq5\end{cases}

The given function is a piecewise function, which is defined as:

\[
f(x) = 
\begin{cases} 
\dfrac{5}{x} & \text{for } x > 5 \\
x - 4 & \text{for } x \leq 5
\end{cases}
\]

This means that the value of \( f(x) \) depends on the value of \( x \). Specifically:

- For \( x > 5 \), the function follows the expression \( f(x) = \dfrac{5}{x} \).
- For \( x \leq 5 \), the function follows the expression \( f(x) = x - 4 \).

If you have a specific question regarding this function (e.g., evaluating it at a particular value, finding limits, or analyzing continuity), feel free to ask!

### Do you want any further details or clarifications? 

Here are some related questions:
1. What is the value of \( f(6) \)?
2. Is this function continuous at \( x = 5 \)?
3. What happens to \( f(x) \) as \( x \) approaches 5 from the right?
4. How would you graph this function?
5. What is the domain and range of this piecewise function?

**Tip:** When working with piecewise functions, always check the behavior at the transition points (in this case, \( x = 5 \)) to ensure continuity and correct interpretation.

f(x) = \begin{cases} \dfrac{5}{x} & \text{for} ~~~~x\gt{5} \\ x-4 & \text{for} ~~~~ x \leq5 \end{cases}

Explore the piecewise function f(x) = 5/x for x > 5 and f(x) = x - 4 for x ≤ 5. Understand its behavior at transition points, analyze continuity, and evaluate limits. Suitable for high school students (Grades 9-12) learning about piecewise functions.

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