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

Question

whats the
Linear or Nonlinear:

Domain:

Range:

Increasing or Decreasing:

End behavior:

Answer 1

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:
  • \( \lim_{s \to 0} A(s) = 0 \)
  • \( \lim_{s \to \infty} A(s) = \infty \)

Answer 2

end behavior write diffrent just numbers

Answer 3

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 \( (\infty, \infty) \)