Question

The equation for the area of a square could be written: A=s2
(4 points)
1) Is this a linear or nonlinear function?

2) What are some of the values in the table where s is the side length and A is the area?

3) When you plot these points, is the graph increasing or decreasing?

4) What numbers would be included in the domain?


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Answer 1

Let's break down your questions regarding the equation for the area of a square, \( A = s^2 \).

1. **Is this a linear or nonlinear function?**
- The equation \( A = s^2 \) is a **nonlinear function**. This is because the relationship between the side length \( s \) and the area \( A \) is quadratic; it involves \( s \) being raised to the power of 2, which indicates a nonlinear relationship.

2. **What are some of the values in the table where s is the side length and A is the area?**
- Here are some values that you can use to create a table:
- If \( s = 0 \), then \( A = 0^2 = 0 \)
- If \( s = 1 \), then \( A = 1^2 = 1 \)
- If \( s = 2 \), then \( A = 2^2 = 4 \)
- If \( s = 3 \), then \( A = 3^2 = 9 \)
- If \( s = 4 \), then \( A = 4^2 = 16 \)
- Table:
| s (side length) | A (area) |
|------------------|----------|
| 0 | 0 |
| 1 | 1 |
| 2 | 4 |
| 3 | 9 |
| 4 | 16 |

3. **When you plot these points, is the graph increasing or decreasing?**
- When you plot the points from the table, the graph is **increasing**. As the side length \( s \) increases, the area \( A \) also increases. Moreover, because \( A = s^2 \) describes a parabola that opens upwards, the function will continue to rise as \( s \) increases.

4. **What numbers would be included in the domain?**
- The domain of the function \( A = s^2 \) consists of all non-negative real numbers. This is because the side length \( s \) must be greater than or equal to 0 (you cannot have a negative side length for a square). Therefore, the domain can be expressed as:
- \( [0, \infty) \) or \( s \geq 0 \).

If you have any additional questions or need further assistance, feel free to ask!