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