https://r2.erweima.ai/mathbot/image/1726801134723jglpvrtl.jpg

The graph shows a function \( f \) with a clear domain and range, and we are asked to express both using interval notation.

### Observing the graph:

1. **Domain**: The domain represents all the possible \( x \)-values for which the function is defined. In the graph:
   - The function starts at \( x = -4 \) and ends at \( x = 2 \).
   - Both endpoints are represented as open circles, meaning that the function does not include these points.
   - Therefore, the domain is \( (-4, 2) \).

2. **Range**: The range represents all the possible \( y \)-values that the function takes.
   - The highest point of the function is around \( y = 4 \) and the lowest point is approximately \( y = -3 \).
   - Again, the endpoints are open, so these values are not included.
   - Therefore, the range is \( (-3, 4) \).

### Final Answer:
- (a) \( \text{Dominio} = (-4, 2) \)
- (b) \( \text{Rango} = (-3, 4) \)

Let me know if you need more details or further clarifications.

---

Here are 5 related questions to deepen your understanding:
1. What is the significance of open vs closed intervals in domain and range notation?
2. How would the domain and range change if the endpoints were closed circles instead of open?
3. Can a function have an unbounded domain or range? Give examples.
4. How can we determine if a function is continuous based on its graph?
5. What is the difference between the domain of a function and the domain of its inverse?

**Tip**: Always check if the endpoints of a graph are open or closed when determining the domain and range, as this can change your answer.

Find the domain and range of the function based on the graph provided, where the function has endpoints at (-4, 4) and (2, -3), both open.

Learn how to find the domain and range of a function using interval notation based on its graph. This problem features open endpoints at (-4, 4) and (2, -3) and is suitable for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation