Question

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 this down step by step based on the equation \( A = s^2 \), where \( A \) is the area of a square and \( s \) is the side length.

1) **Is this a linear or nonlinear function?**
The function \( A = s^2 \) is a **nonlinear function**. This is because it involves \( s \) raised to the power of 2 (a quadratic relationship), which means the graph of the function is a parabola opening upwards and not a straight line.

2) **What are some of the values in the table where s is the side length and A is the area?**
Here are some example values you could include in the table:

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

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. This is characteristic of a quadratic function where the outputs grow larger as the inputs increase.

4) **What numbers would be included in the domain?**
The domain of the function \( A = s^2 \) includes all non-negative real numbers, as the side length \( s \) of a square cannot be negative. Therefore, the domain is \( [0, \infty) \).

In summary:
1) Nonlinear function
2) Sample values: (0, 0), (1, 1), (2, 4), (3, 9), (4, 16), (5, 25)
3) The graph is increasing.
4) Domain is \( [0, \infty) \).