no explain The table shows a function. Is the function linear or nonlinear?
x	y
1	0
4
3
5
4
10	7

To determine whether the function is linear or nonlinear, we need to check if the changes in \( x \) and \( y \) follow a constant rate (i.e., the same difference each time).

Given:
- When \( x = 1 \), \( y = 0 \)
- When \( x = 4 \), \( y = 3 \)
- When \( x = 10 \), \( y = 7 \)

We check the differences:

1. From \( x = 1 \) to \( x = 4 \), \( \Delta x = 3 \) and \( \Delta y = 3 \).
2. From \( x = 4 \) to \( x = 10 \), \( \Delta x = 6 \) and \( \Delta y = 4 \).

Since the changes in \( y \) with respect to \( x \) are not constant, the function is **nonlinear**.

Do you want more details or have any questions?

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Here are 5 relative questions:
1. How can you identify linear functions from tables?
2. What is the formula for a linear function?
3. Can a function with variable rate changes be linear?
4. How can slope help in determining a function’s linearity?
5. What are some common examples of nonlinear functions?

**Tip:** A linear function will always have a constant rate of change, meaning equal increments in \( x \) will lead to equal increments in \( y \).

The table shows a function. Is the function linear or nonlinear? x y 1 0 4 3 5 4 10 7

Learn how to determine whether a function is linear or nonlinear by analyzing a table of values with points like (1, 0), (4, 3), and (10, 7). This problem explains the concept of rate of change and introduces the slope formula. Suitable for students in Grades 6-8.

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