Here is the graph of the piecewise function \( f(x) \):

- For \( x < 0 \), \( f(x) = -1 \) is a constant value.
- For \( 0 \leq x \leq 4 \), \( f(x) = 2x - 8 \) is a linear function.
- For \( x > 4 \), \( f(x) = \sqrt{x - 4} \) is a square root function.

Notice the discontinuities and the different slopes as the function transitions between different segments.

Do you want further details or have any questions?

### Additional Questions
1. Is \( f(x) \) continuous at \( x = 0 \) and \( x = 4 \)?
2. Can we calculate the left-hand and right-hand limits at \( x = 0 \) and \( x = 4 \)?
3. How does \( f(x) \) behave as \( x \to \infty \)?
4. What is the derivative of each piece of the function in its respective domain?
5. Can you determine if the function is increasing or decreasing in each region?

### Tip
For piecewise functions, always check the limits and continuity at transition points, as these often reveal key properties of the function.

Explore the graph and properties of the piecewise function f(x), including continuity at critical points, limit calculations, and derivative analysis. This problem covers key concepts in calculus and function theory, suitable for advanced high school students.

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