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find the domain and range using set-bulider notation

The image shows a graph of a linear function. To find the domain and range using set-builder notation, let's analyze the graph:

### **Domain:**
The domain represents all possible values of \( x \) for which the function is defined. The graph is a straight line that extends infinitely in both directions along the \( x \)-axis.

**Domain in Set-Builder Notation:**
\[ \{ x \mid x \in \mathbb{R} \} \]
This notation means that the domain includes all real numbers.

### **Range:**
The range represents all possible values of \( y \) that the function can take. Since the graph is a straight line that extends infinitely along the \( y \)-axis, the range also includes all real numbers.

**Range in Set-Builder Notation:**
\[ \{ y \mid y \in \mathbb{R} \} \]
This means that the range includes all real numbers.

**Summary:**
- **Domain:** \( \{ x \mid x \in \mathbb{R} \} \)
- **Range:** \( \{ y \mid y \in \mathbb{R} \} \)

Would you like further details or have any questions? 

Here are 5 questions that expand on this topic:

1. How can the slope of the line in the graph be determined?
2. What is the significance of the intercepts on the graph?
3. How would the domain and range change if the line were not continuous?
4. Can you write the equation of the line based on its graph?
5. What are some real-world applications of finding the domain and range of a function?

**Tip:** Understanding how to read graphs and express domains and ranges in set-builder notation is crucial for analyzing functions in algebra and calculus.

Learn how to find the domain and range of a function using set-builder notation with a step-by-step explanation. Understand the concept of domain as all possible values of x and range as all possible values of y. Suitable for students in Grades 9-12.

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