i. For left-endpoint and midpoint rectangles, let the index start at $0$ and end at $n - 1$.
For right-endpoint rectangles, let the index start at $1$ and end at $n$.
$n = \text{number of rectangles}$.

$\text{ii. The }\frac{1}{2}\text{ represents the WIDTH/BASE of all rectangles.}$

To determine the width of each rectangle, divide the domain by the number of rectangles:

$\frac{7-3}{1}=\frac{1}{2}.$

$\text{Each rectangle has a width, }\Delta x \text{ is } \frac{1}{2}.$

iii. The transformed function represents the HEIGHT of each rectangle.
For left- and right-endpoint rectangles, the heights are represented by $f(a + \Delta xi)$.
For midpoint rectangles, the heights are represented by

$f \left(a+\frac{\Delta x}{2}i\right).$

$a = \text{starting value}$
$\Delta x = \text{width of each rectangle}$.