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The image shows two questions asking about the range of functions based on given graphs:

### First Question:
The graph shows a "V" shape, resembling an absolute value function. The graph's lowest point is at (0, -2), and it opens upwards.

**Possible Answers for the Range:**
- A: \( y \geq -2 \)
- B: \( y \geq 0 \)
- C: \( y \leq 2 \)
- D: \( y \geq 2 \)

**Correct Answer:**
The range of the function is \( y \geq -2 \), so the correct choice is **A**.

### Second Question:
The graph shows a circle centered at (2, 0) with a radius of 4.

**Possible Answers for the Range:**
- A: \( -4 \leq y \leq 4 \)
- B: \( y \geq -4 \)
- C: \( y \leq 4 \)
- D: \( y \geq 4 \)

**Correct Answer:**
The range of the circle is from -4 to 4 along the y-axis, so the correct choice is **A**.

Would you like further details or have any questions?

### Related Questions:
1. What is the general formula for the range of an absolute value function?
2. How can you determine the range of a function from its graph?
3. What are the properties of a circle in the coordinate plane?
4. How can you find the range of other types of functions like quadratic or exponential?
5. What role does the vertex or center of a graph play in determining its range?

**Tip:** The range of a function tells you all possible y-values that the function can output. Look for the lowest and highest points on the graph to identify it.

What is the range of the following functions based on the graphs provided?

Learn how to find the range of absolute value functions and circle equations from their graphs. This problem explains how to calculate the range, using the graph of an absolute value function and a circle. Suitable for students in Grades 8-10.

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