Answer: all three statements are true
Step-by-step explanation:
The question states that the function A models the rectangle's area as a function of its width. We need to determine which statements are true.
Let's consider the properties of the area of a rectangle in relation to its width:
1. The area of a rectangle is calculated by multiplying its length by its width. Therefore, the function A can be written as A(w) = lw, where w represents the width and l represents the length.
2. The area of a rectangle is always non-negative. This means that the area cannot be negative or zero for any positive value of the width. Therefore, A(w) > 0 for all positive values of w.
3. The area of a rectangle increases as the width increases, assuming the length remains constant. This is because a larger width results in a larger area. Therefore, if we compare two positive values of the width, w1 and w2, where w1 < w2, we have A(w1) < A(w2).
Based on these properties, the true statements are:
- Statement 1: The function A can be written as A(w) = lw, where w represents the width and l represents the length.
- Statement 2: A(w) > 0 for all positive values of w.
- Statement 3: If we compare two positive values of the width, w1 and w2, where w1 < w2, we have A(w1) < A(w2).
Therefore, all three statements are true.