https://file.aiquickdraw.com/mathbot/file/1726828389300dqvomive.jpg

The image shows a graph of a piecewise linear function \( f(x) \), and the task asks for the value of \( \lim_{x \to 2} f(x) \).

### Step-by-step analysis:

1. **Left-hand limit (\( x \to 2^- \)):**
   - As \( x \) approaches 2 from the left (i.e., values slightly less than 2), the function is represented by a line that approaches \( y = 3 \) at \( x = 2 \) (the solid point at \( (2, 3) \)).

2. **Right-hand limit (\( x \to 2^+ \)):**
   - As \( x \) approaches 2 from the right (i.e., values slightly greater than 2), the function is represented by a line that approaches \( y = 1 \) at \( x = 2 \) (the open circle at \( (2, 1) \)).

3. **Conclusion:**
   - Since the left-hand limit is 3 and the right-hand limit is 1, the limit does not exist because \( \lim_{x \to 2^-} f(x) \neq \lim_{x \to 2^+} f(x) \).

The correct answer is therefore **"d. Tidak Ada"** (which means "does not exist").

Let me know if you want more details or have any questions.

### 5 Related Questions:
1. What are the conditions for the limit of a function to exist at a point?
2. How do you calculate one-sided limits from a graph?
3. What is the difference between a continuous function and a function with discontinuities?
4. Can a function have a limit at a point if there is a jump discontinuity?
5. How do open and closed points on a graph affect limit evaluation?

### Tip:
Always check both the left-hand and right-hand limits when evaluating the limit of a piecewise function at a specific point to determine if the overall limit exists.

Tentukan lim x→2 f(x) berdasarkan grafik yang ditunjukkan dalam gambar.

Evaluate the limit of a piecewise linear function at x = 2 using graphical analysis. This involves understanding one-sided limits and continuity. Suitable for high school students in Grades 10-12.

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