A right rectangular prism has a height of 9 inches. The length of the prism's base

Choice D is correct. The volume of a right rectangular prism can be represented by a function $V$ that gives the volume of the prism, in cubic inches, in terms of the length of the prism's base. The volume of a right rectangular prism is equal to the area of its base times its height. It's given that the length of the prism's base is $x$ inches, which is $7$ inches more than the width of the prism's base. This means that the width of the prism's base is $x-7$ inches. It follows that the area of the prism's base, in square inches, is $x\left(x-7\right)$ and the volume, in cubic inches, of the prism is $x\left(x-7\right)\left(9\right)$. Thus, the function $V$ that gives the volume of this right rectangular prism, in cubic inches, in terms of the length of the prism's base, $x$, is $V\left(x\right)=9x\left(x-7\right)$.

Choice A is incorrect. This function would give the volume of the prism if the height were $9$ inches more than the length of its base and the width of the base were $7$ inches more than its length.

Choice B is incorrect. This function would give the volume of the prism if the height were $9$ inches more than the length of its base.

Choice C is incorrect. This function would give the volume of the prism if the width of the base were $7$ inches more than its length, rather than the length of the base being $7$ inches more than its width.