Hey rectangle has a white represented by the function f of x equals X and the width represented by the function g of x equals x + 3 were both functions are in feet calculate at times g of X and state what it represents

Answer 1

To calculate the area of the rectangle formed by the height and width functions you provided, we need to multiply the two functions together:

1. Height \( f(x) \) is given by: \[ f(x) = x \]

2. Width \( g(x) \) is given by: \[ g(x) = x + 3 \]

To find the area \( A(x) \) of the rectangle, we multiply the height and width:

\[ A(x) = f(x) \cdot g(x) = x \cdot (x + 3) \]

Expanding this expression:

\[ A(x) = x^2 + 3x \]

What it represents: The function \( A(x) = x^2 + 3x \) represents the area of the rectangle in square feet as a function of \( x \). Here, \( x \) is the height of the rectangle in feet, and the width is \( x + 3 \) feet, so the area changes as the height \( x \) changes.