The function A = s^2 giving the area of a square as a function of its side length

whats the
Linear or Nonlinear:

Domain:

Range:

Increasing or Decreasing:

End behavior:

3 answers

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:

  1. Linear or Nonlinear:

    • The function is Nonlinear because it is a quadratic function (the variable \( s \) is squared).
  2. 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 \( [0, \infty) \).
  3. Range:

    • The range of the function is \( A \geq 0 \). Since the area is always non-negative, the range in interval notation is \( [0, \infty) \).
  4. 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.
  5. 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:
      • \( \lim_{s \to 0} A(s) = 0 \)
      • \( \lim_{s \to \infty} A(s) = \infty \)

To summarize:

  • Linear or Nonlinear: Nonlinear
  • Domain: \( [0, \infty) \)
  • Range: \( [0, \infty) \)
  • Increasing or Decreasing: Increasing
  • End Behavior:
    • \( \lim_{s \to 0} A(s) = 0 \)
    • \( \lim_{s \to \infty} A(s) = \infty \)
end behavior write diffrent just numbers

Sure! Here’s the end behavior represented with just numbers:

  • End Behavior:
    • As \( s \to 0 \), \( A \to 0 \)
    • As \( s \to \infty \), \( A \to \infty \)

In numerical format:

  • \( (0, 0) \) and \( (\infty, \infty) \)
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