https://file.aiquickdraw.com/mathbot/file/1725379301256adll08kv.jpg

Let's analyze the graph in the image and answer the questions accordingly.

### 1. Domain Interval:
The domain of a function is the set of all possible input values (x-values). Based on the graph:

- The function exists from \(x = -4\) to \(x = 4\).

Thus, the domain interval is:
\[ \text{Domain Interval} = [-4, 4] \]

### 2. Range Interval:
The range of a function is the set of all possible output values (y-values). From the graph:

- The minimum value of \( y \) appears to be \( y = -2 \).
- The maximum value of \( y \) appears to be \( y = 3 \).

So, the range interval is:
\[ \text{Range Interval} = [-2, 3] \]

### 3. Domain SB (Set Builder notation):
The domain in set-builder notation specifies the set of x-values. Based on the domain interval:
\[ \text{Domain SB} = \{ x \mid -4 \leq x \leq 4 \} \]

### 4. Range SB (Set Builder notation):
The range in set-builder notation specifies the set of y-values. Based on the range interval:
\[ \text{Range SB} = \{ y \mid -2 \leq y \leq 3 \} \]

### 5. Find \( f(0) \):
To find \( f(0) \), locate the y-value corresponding to \( x = 0 \) on the graph:

- From the graph, when \( x = 0 \), \( y = 2 \).

So:
\[ f(0) = 2 \]

### 6. Find \( f(-2) \):
To find \( f(-2) \), locate the y-value corresponding to \( x = -2 \) on the graph:

- From the graph, when \( x = -2 \), \( y = 1 \).

So:
\[ f(-2) = 1 \]

---

Would you like further details or explanations on any of these solutions?

### Related Questions:
1. What would be the domain and range if the function was shifted 2 units up?
2. How would the graph change if reflected across the y-axis?
3. What is the significance of a function being continuous over its domain?
4. How do we determine the maximum and minimum values of a function from its graph?
5. What is the importance of understanding the domain and range in real-world applications?

### Tip:
Always double-check the endpoints of a graph when determining the domain and range, especially if the function includes open or closed intervals.

Analyze the graph provided in the image and answer the following questions: Determine the domain and range intervals, express the domain and range in set-builder notation, and find the values of f(0) and f(-2).

Learn how to analyze a graph to determine the domain and range, express them in set-builder notation, and find specific function values such as f(0) and f(-2). This problem is ideal for students in Grades 9-12 who are studying functions and graph interpretation.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation