Question

The equation for the area of a square could be written: A=s2 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

1. The equation for the area of a square, \( A = s^2 \), represents a nonlinear function. This is because the area \( A \) is proportional to the square of the side length \( s \), leading to a parabolic relationship when graphed.

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

| Side Length (s) | Area (A) | |------------------|-----------| | 0 | 0 | | 1 | 1 | | 2 | 4 | | 3 | 9 | | 4 | 16 | | 5 | 25 |

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

4. The domain of the function (possible values for \( s \)) includes all non-negative real numbers, since a square cannot have a negative side length. Therefore, the domain is \( [0, \infty) \).