Let's analyze the function \( A = s^2 \) where \( A \) is the area of the square and \( s \) is the side length.
Linear or Nonlinear:
- Nonlinear: The function \( A = s^2 \) is a quadratic function, which is nonlinear because it does not form a straight line when graphed.
Domain:
- Domain: Since \( s \) represents the side length of a square, it must be non-negative. Therefore, the domain is \( [0, \infty) \).
Range:
- Range: The area \( A \) is also non-negative, as the area cannot be negative. Thus, the range is \( [0, \infty) \).
Increasing or Decreasing:
- Increasing: The function \( A = s^2 \) is increasing for \( s \geq 0 \) because as \( s \) increases, \( A \) increases. The derivative \( \frac{dA}{ds} = 2s \) is positive for \( s > 0 \).
End behavior:
- 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:
- As \( s \to 0 \): \( A \to 0 \)
- As \( s \to \infty \): \( A \to \infty \)
In summary:
- Linear or Nonlinear: Nonlinear
- Domain: [0, ∞)
- Range: [0, ∞)
- Increasing or Decreasing: Increasing
- End behavior:
- \( A \to 0 \) as \( s \to 0 \)
- \( A \to \infty \) as \( s \to \infty \)