Question

The equation for the area of a square could be written: A=s^2
(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?

Answer 1

For 4, is the numbers that would be included in the domain, positive or negative?

Answer 2

1) The equation \( A = s^2 \) represents a nonlinear function because the area \( A \) is a quadratic function of the side length \( s \).

2) Here are some values for the table where \( s \) is the side length and \( A \) is the area:

| s | A (s²) |
|-------|-----------|
| 0 | 0 |
| 1 | 1 |
| 2 | 4 |
| 3 | 9 |
| 4 | 16 |
| 5 | 25 |
| 6 | 36 |

3) When you plot these points, the graph is increasing because as the side length \( s \) increases, the area \( A \) also increases.

4) The domain of this function consists of all non-negative real numbers since the side length \( s \) cannot be negative. Thus, the domain is \( s \geq 0 \) or in interval notation, \( [0, +\infty) \).

Answer 3

For the equation \( A = s^2 \), the side length \( s \) represents the length of the sides of a square, which must be non-negative. Therefore, the numbers included in the domain are:

- **Non-negative real numbers**, which means the domain includes **zero and positive numbers** only (i.e., \( s \geq 0 \)).

Negative values would not make sense in the context of side lengths, so they are **not included** in the domain. In interval notation, the domain is \( [0, +\infty) \).