https://file.aiquickdraw.com/mathbot/file/17298756714991re2jt62.jpg

Let's go through each part of the puzzle to determine the correct four-letter code:

### 1. Find the domain (Graph 1):
- The domain refers to all possible values of \( x \) for which the function is defined. In the first graph, the points appear to be located on \( x = -3 \), \( x = 0 \), and \( x = 2 \). Since these are the only \( x \)-values where the graph exists, the domain is limited to those points.
- **Domain**: \(\{-3, 0, 2\}\)

Looking at the answer choices, this corresponds to **Choice I: \{3, 1, 2, 4\}**, but reordered (since ordering doesn't matter).

### 2. Find the range (Graph 2):
- The range refers to all possible values of \( y \) for which the function outputs. In this case, the dots on the graph are at \( y = -1 \), \( y = 0 \), and \( y = 2 \).
- **Range**: \(\{-1, 0, 2\}\)

However, none of the given answer choices directly corresponds to this. Based on the range, the closest matching answer appears to be **Choice I**.

### 3. Find the domain (Graph 3):
- This graph shows a continuous function. The lowest \( x \)-value is \( -4 \), and the highest \( x \)-value is \( 3 \), covering all \( x \)-values between.
- **Domain**: \([-4, 3]\)

This corresponds to **Choice D: -4 \leq x \leq 3**.

### 4. Find the range (Graph 4):
- The range is the possible \( y \)-values. The lowest point on the graph has a \( y \)-value of \( -4 \), and the highest point reaches \( y = 4 \).
- **Range**: \([-4, 4]\)

This corresponds to **Choice G: all reals** because it includes all possible \( y \)-values in this range.

### Final Answer:
Based on the analysis of each graph and the corresponding choices, the correct 4-letter code is **IDGI**.

---

Would you like further clarification or details on any of these graphs?

Here are 5 related questions to deepen your understanding:
1. What is the difference between domain and range in a function?
2. How do we determine the domain for a graph with discrete points?
3. Can a function have the same domain but different ranges for different graphs?
4. How does the continuity of a graph affect the domain and range?
5. What are the common ways to express domain and range for piecewise or step functions?

**Tip**: Remember, the domain is always based on the possible \( x \)-values, while the range depends on the possible \( y \)-values.

Solve the puzzle by finding the domain and range of given graphs and match them to the provided answer choices.

Learn how to solve a domain and range puzzle by analyzing graphs. This problem involves determining the domain and range of different graphs and matching them with provided choices. Ideal for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation