https://file.aiquickdraw.com/mathbot/file/1734029760174l4lxijei.jpg

From the uploaded image, the question asks to determine whether each function is linear or nonlinear. Let's evaluate **Function A** and **Function B** step by step:

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### **Function A**:
From the table of values:

| x | y |
|---|---|
| 0 | 2 |
| 1 | 3 |
| 2 | 6 |
| 3 | 11 |

To check if this is a **linear function**, compute the difference in \( y \)-values for successive \( x \)-values. If the differences are constant, the function is linear.

1. From \( x = 0 \) to \( x = 1 \): \( y = 3 - 2 = 1 \)
2. From \( x = 1 \) to \( x = 2 \): \( y = 6 - 3 = 3 \)
3. From \( x = 2 \) to \( x = 3 \): \( y = 11 - 6 = 5 \)

The differences in \( y \)-values are **not constant** (\( 1, 3, 5 \)). Thus, **Function A is nonlinear**.

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### **Function B**:
From the graph, the function forms a straight line that has a constant slope. This is the defining property of a **linear function**.

Thus, **Function B is linear**.

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### Final Answer:
- **Function A is a nonlinear function.**
- **Function B is a linear function.**

Would you like further explanation or have any questions? 😊  

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### Related Questions:
1. How do you determine if a function is linear from a table of values?
2. Can a nonlinear function ever have a constant slope?
3. What are the key differences between linear and nonlinear functions in a graph?
4. How would the equation of Function B look like if written as \( y = mx + b \)?
5. What are examples of real-world situations modeled by nonlinear functions?

### Tip:
When working with a graph, a straight line always indicates a linear function, while curves or irregular patterns represent nonlinear functions.

Tell whether each function is linear or nonlinear using a table of values for Function A and a graph for Function B.

Learn how to determine if functions are linear or nonlinear using tables and graphs. For Function A, analyze y-value changes in the table. For Function B, check the straight line on the graph. Suitable for Grades 6-8 students.

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