The function \( A = s^2 \) represents the area \( A \) of a square as a function of its side length \( s \). Let's analyze the function in terms of the specified criteria:
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Linear or Nonlinear:
- The function is Nonlinear because it is a quadratic function (the variable \( s \) is squared).
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Domain:
- The domain of the function is \( s \geq 0 \). In practical terms, the side length of a square cannot be negative, so the domain in interval notation is \( [0, \infty) \).
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Range:
- The range of the function is \( A \geq 0 \). Since the area is always non-negative, the range in interval notation is \( [0, \infty) \).
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Increasing or Decreasing:
- The function \( A = s^2 \) is increasing for \( s \geq 0 \) because as the side length \( s \) increases, the area \( A \) also increases.
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End Behavior:
- As \( s \) approaches infinity (\( s \to \infty \)), \( A \) also approaches infinity (\( A \to \infty \)). As \( s \) approaches 0 (\( s \to 0 \)), \( A \) approaches 0 (\( A \to 0 \)). Therefore, the end behavior can be summarized as:
- \( \lim_{s \to 0} A(s) = 0 \)
- \( \lim_{s \to \infty} A(s) = \infty \)
- As \( s \) approaches infinity (\( s \to \infty \)), \( A \) also approaches infinity (\( A \to \infty \)). As \( s \) approaches 0 (\( s \to 0 \)), \( A \) approaches 0 (\( A \to 0 \)). Therefore, the end behavior can be summarized as:
To summarize:
- Linear or Nonlinear: Nonlinear
- Domain: \( [0, \infty) \)
- Range: \( [0, \infty) \)
- Increasing or Decreasing: Increasing
- End Behavior:
- \( \lim_{s \to 0} A(s) = 0 \)
- \( \lim_{s \to \infty} A(s) = \infty \)