https://file.aiquickdraw.com/mathbot/file/1724568236211ni8op0pg.jpg

State the domain and range for ach graph and then tellif the graph is a function (wite yes or no). in set builder notation

The graph provided shows a curve that appears to be a polynomial function.

### 1. **Domain**:
The domain of the graph includes all the possible x-values for which the function is defined. Since the graph extends infinitely to the left and right along the x-axis, the domain is all real numbers.

**Domain in set-builder notation**:
\[ \{ x \in \mathbb{R} \} \]

### 2. **Range**:
The range includes all the possible y-values that the function can take. Observing the graph, the curve appears to reach infinitely upward and downward, covering all possible y-values.

**Range in set-builder notation**:
\[ \{ y \in \mathbb{R} \} \]

### 3. **Is the Graph a Function?**:
To determine if the graph is a function, we can apply the **Vertical Line Test**. If any vertical line crosses the graph at more than one point, then the graph is **not** a function. However, in this case, every vertical line crosses the graph at exactly one point.

**Answer**: Yes, the graph is a function.

---

Would you like more details or have any questions about this? Here are some related questions:

1. What are the key characteristics of a polynomial function's graph?
2. How does the degree of a polynomial affect the graph's shape?
3. Can you identify the turning points on the graph and explain their significance?
4. How do you determine the end behavior of polynomial functions?
5. What does it mean for a function to have symmetry, and does this graph exhibit symmetry?

**Tip**: When analyzing graphs, always check for key features like intercepts, turning points, and end behavior to better understand the function.

Explore the concepts of domain, range, and function in graphs with a detailed explanation and examples. Learn how to determine the domain and range of a function using set builder notation. Understand the Vertical Line Test to determine if a graph represents a function. Suitable for high school students studying functions and graphing.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation