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The function \( A = s^2 \) is a nonlinear function because the area (\( A \)) is proportional to the square of the side length (\( s \)). In a linear function, the relationship would be of the form \( A = ms + b \) (where \( m \) is a constant slope and \( b \) is a constant). However, in this case, the exponent is 2.
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Some values in the table could look like this, where \( s \) is the side length and \( A \) is the area:
| \( s \) | \( A \) | |---------|----------| | 0 | 0 | | 1 | 1 | | 2 | 4 | | 3 | 9 | | 4 | 16 | | 5 | 25 |
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When you plot these points, the graph is increasing. As \( s \) increases, the value of \( A \) (the area) increases, and it does so at an increasing rate due to the quadratic nature of the function.
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The numbers included in the domain are all non-negative real numbers, which can be represented as \( [0, \infty) \). This is because side lengths cannot be negative and can include zero (representing a square with no area).
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