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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?

3 answers

  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 |

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

  2. 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, \( [0, +\infty) \).

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

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 \( [0, +\infty) \).