Graph the function on the interval [-5, 2). f(x)=[[x+4]]

Here's the graph of the function \( f(x) = \left\lfloor x + 4 \right\rfloor \) on the interval \([-5, 2)\). The function jumps at integer values of \(x\), and the floor function steps down to the nearest integer at each discontinuity.

Would you like any further details or have any questions?

Here are five related questions:
1. What happens to \( f(x) \) when \( x = 2 \)?
2. How would the graph change if \( f(x) = \lceil x + 4 \rceil \) (the ceiling function)?
3. What is the difference between the floor and ceiling functions?
4. How does the function behave for negative values of \( x \)?
5. How would the function change if the interval were extended to \( [0, 5) \)?

**Tip:** The floor function always "rounds down" to the nearest integer.

Explore how to graph the floor function f(x) = ⌊x + 4⌋ on the interval [-5, 2). This problem covers key mathematical concepts, including piecewise functions and properties of the floor function. Suitable for students in Grades 9-12.

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