The function \( f(w)=6 w^{2} \) gives the area of a rectangle, in square feet \( \left(\mathrm{ft}^{2}\right) \), if its width is \( w \mathrm{ft} \) and its length is 6 times its width. Which of the following is the best interpretation of \( f(14)=1,176 \) ? A) If the width of the rectangle is 14 ft , then the area of the rectangle is \( 1,176 \mathrm{ft}^{2} \). B) If the width of the rectangle is 14 ft , then the length of the rectangle is \( 1,176 \mathrm{ft} \). C) If the width of the rectangle is \( 1,176 \mathrm{ft} \), then the length of the rectangle is \( 14 \mathrm{ft} \). D) If the width of the rectangle is \( 1,176 \mathrm{ft} \), then the area of the rectangle is \( 14 \mathrm{ft}^{2} \).

To interpret \( f(14) = 1,176 \) in the context of the function \( f(w) = 6w^2 \), we need to understand what the function represents. The function \( f(w) \) gives the area of a rectangle where: - \( w \) is the width of the rectangle in feet. - The length of the rectangle is \( 6 \) times the width. Now, let's calculate \( f(14) \): \[ f(14) = 6(14^2) = 6(196) = 1,176 \text{ ft}^2 \] This means that when the width of the rectangle is \( 14 \) feet, the area of the rectangle is \( 1,176 \) square feet. Now, let's analyze the options: A) If the width of the rectangle is 14 ft, then the area of the rectangle is \( 1,176 \mathrm{ft}^{2} \). **This is correct.** B) If the width of the rectangle is 14 ft, then the length of the rectangle is \( 1,176 \mathrm{ft} \). **This is incorrect.** The length is \( 6 \times 14 = 84 \) ft, not \( 1,176 \) ft. C) If the width of the rectangle is \( 1,176 \mathrm{ft} \), then the length of the rectangle is \( 14 \mathrm{ft} \). **This is incorrect.** The width cannot be \( 1,176 \) ft based on the function. D) If the width of the rectangle is \( 1,176 \mathrm{ft} \), then the area of the rectangle is \( 14 \mathrm{ft}^{2} \). **This is incorrect.** The area would be much larger if the width were \( 1,176 \) ft. Thus, the best interpretation of \( f(14) = 1,176 \) is: **A) If the width of the rectangle is 14 ft, then the area of the rectangle is \( 1,176 \mathrm{ft}^{2} \).**