The function f w = 6 w 2 gives the area of a rectangle, in  

Choice A is correct. The function $f$ gives the area of the rectangle, in ${\text{ft}}^2$, if its width is $w \text{ft}$. Since the value of $f\left(14\right)$ is the value of $f\left(w\right)$ if $w=14$, it follows that $f\left(14\right)=\mathrm{1,176}$ means that $f\left(w\right)$ is $\mathrm{1,176}$ if $w=14$. In the given context, this means that if the width of the rectangle is $14 \text{ft}$, then the area of the rectangle is $\mathrm{1,176} {\text{ft}}^2$.

Choice B is incorrect and may result from conceptual errors.

Choice C is incorrect and may result from conceptual errors.

Choice D is incorrect and may result from interpreting $f\left(w\right)$ as the width, in $\text{ft}$, of the rectangle if its area is $w {\text{ft}}^2$, rather than as the area, in ${\text{ft}}^2$, of the rectangle if its width is $w \text{ft}$.