https://file.aiquickdraw.com/mathbot/file/1728416438219hbp4rry2.jpg

Let's analyze the graph you provided:

1. **Vertical Line Test**: This test helps determine whether a curve is a function of \( x \). If any vertical line intersects the curve at more than one point, the curve is **not** a function of \( x \). Upon inspecting the graph, it appears that no vertical line would intersect the curve more than once at any point. Therefore, **the curve is a function of \( x \)**.

2. **Domain**: The domain of a function is the set of all possible \( x \)-values for which the function is defined. Looking at the graph, the \( x \)-values range from \( -4 \) to \( 4 \), so the domain in interval notation is:
   \[
   \text{Domain} = [-4, 4]
   \]

3. **Range**: The range is the set of all possible \( y \)-values the function can take. From the graph, the \( y \)-values range from \( -4 \) to \( 4 \), so the range in interval notation is:
   \[
   \text{Range} = [-4, 4]
   \]

### Summary:
- The curve **is** a function of \( x \).
- **Domain**: \([-4, 4]\)
- **Range**: \([-4, 4]\)

Would you like any further explanation or details?

Here are 5 related questions for deeper understanding:
1. What are some other methods for determining if a curve is a function besides the vertical line test?
2. How would the domain and range change if the curve extended beyond \( x = 4 \) or \( y = 4 \)?
3. Can a function ever have more than one \( y \)-value for a single \( x \)-value?
4. How would you find the inverse of a function, and what would be the domain and range of the inverse?
5. Why is it important to express the domain and range in interval notation?

**Tip**: When analyzing the domain and range, always pay attention to the extreme points of the graph to capture the full scope of possible values.

Use the Vertical Line Test to determine whether the curve is the graph of a function of x. If the curve is a function, state the domain and range.

Learn how to apply the Vertical Line Test to determine if a curve is a function of x, and how to find the domain and range from the graph. Includes a step-by-step solution and examples. Suitable for high school students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation