https://file.aiquickdraw.com/mathbot/file/17286938250577f9wdgh3.jpg

Let's analyze the graph and answer the questions.

### (a) **Domain and Range** of the function \( f \):
- **Domain**: The domain of a function is the set of all possible \( x \)-values (horizontal axis) for which the function is defined. From the graph, the function starts around \( x = -2 \) and ends around \( x = 3 \). So, the domain is approximately:
  \[
  [-2, 3]
  \]

- **Range**: The range is the set of all possible \( y \)-values (vertical axis) that the function takes. From the graph, the lowest point is around \( y = -1 \) and the highest point is around \( y = 2 \). So, the range is approximately:
  \[
  [-1, 2]
  \]

### (b) **Intervals where \( f \) is increasing and decreasing**:
- **Increasing**: A function is increasing where the graph is going upwards as \( x \) increases. From the graph, the function is increasing from \( x = -2 \) to \( x = -1 \), and again from \( x = 1 \) to \( x = 2 \). So the intervals where the function is increasing are:
  \[
  (-2, -1) \cup (1, 2)
  \]

- **Decreasing**: A function is decreasing where the graph is going downwards as \( x \) increases. From the graph, the function is decreasing from \( x = -1 \) to \( x = 1 \), and again from \( x = 2 \) to \( x = 3 \). So the intervals where the function is decreasing are:
  \[
  (-1, 1) \cup (2, 3)
  \]

### Final answers:
- **Domain**: \( [-2, 3] \)
- **Range**: \( [-1, 2] \)
- **Increasing**: \( (-2, -1) \cup (1, 2) \)
- **Decreasing**: \( (-1, 1) \cup (2, 3) \)

Would you like further details or clarifications on any part of this? 

Here are 5 related questions to explore:
1. How do you determine the domain and range for more complex functions?
2. What are the conditions for a function to be considered increasing or decreasing?
3. How would vertical or horizontal shifts affect the domain and range of a function?
4. Can a function be increasing and decreasing on the same interval?
5. How can you identify local maxima and minima from a graph?

**Tip**: When identifying where a function increases or decreases, focus on the behavior of the graph (going up or down) as you move from left to right along the \( x \)-axis.

The graph of a function f is given. Estimate the domain, range, and intervals of increasing and decreasing behavior.

Analyze the graph of a function to estimate its domain, range, and identify where the function is increasing and decreasing. This solution involves understanding core concepts of functions, intervals, and graph analysis. Suitable for 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