https://r2.erweima.ai/mathbot/image/1726676166421hxo6jjr4.jpg

The image shows a graph with several disconnected horizontal line segments. Based on the characteristics of the graph, here is the analysis of the function depicted:

- The graph consists of horizontal line segments where each value of \(x\) has a corresponding distinct \(y\)-value. For example, for \(x = -2\), the \(y\)-value is \( -2 \), and for \(x = 0\), the \(y\)-value is 0. This type of graph resembles the "ceiling function" (fungsi atap), which rounds numbers up to the nearest integer.

### Let's evaluate the options:
1. **Grafik fungsi lantai**: This is the floor function, which rounds down. The graph does not match the floor function as the values are rounded up instead.
2. **Grafik fungsi atap**: This matches the ceiling function (values rounded up). So this is the correct option.
3. **Fungsi surjektif**: This refers to a surjective (onto) function where every possible \(y\)-value in the codomain is mapped by at least one \(x\)-value. The graph only maps to certain values, so it is **not surjective**.
4. **Fungsi injektif**: This refers to an injective (one-to-one) function where each \(x\)-value maps to a unique \(y\)-value, and no two different \(x\)-values map to the same \(y\)-value. Since horizontal lines exist (same \(y\)-value for different \(x\)-values), the function is **not injective**.
5. **Bukan fungsi**: The graph passes the vertical line test (each \(x\) has a unique \(y\)-value), so it is a valid function. Therefore, it **is a function**.

### Conclusion:
The correct statement is:
- **Grafik fungsi atap** (ceiling function)

Would you like further details or clarifications?

Here are 5 related questions:
1. What is the difference between the ceiling and floor functions?
2. Can a function be both injective and surjective? If so, what is it called?
3. How can you visually identify a surjective function from a graph?
4. What is the significance of the vertical line test for functions?
5. How does rounding behavior affect the graphical representation of functions?

**Tip:** When determining if a graph represents a function, always check the vertical line test first.

Pernyataan yang benar tentang fungsi dengan grafik seperti pada gambar.

Explore the characteristics of the ceiling function graph through a detailed breakdown of the image provided. This includes discussions on the injectivity and surjectivity of the function, and an explanation of how the vertical line test proves the graph represents a valid function. Suitable for students in Grades 9-12.

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