To understand why the correct answer is option 'C' (Step function), let's first define what a step function is and how it relates to the given functions f and g.

Step Function:
A step function is a function that remains constant on each interval between the points where it changes value. It is a piecewise-defined function consisting of a finite number of constant segments.

Given Functions f and g:
The functions f and g are defined as step functions on a given rectangle. Let's denote them as follows:
f(x) = a1 on interval I1, a2 on interval I2, ..., an on interval In
g(x) = b1 on interval J1, b2 on interval J2, ..., bm on interval Jm

where a1, a2, ..., an, b1, b2, ..., bm are constants, and I1, I2, ..., In, J1, J2, ..., Jm are intervals.

Multiplying by Constants:
Now, let's consider the product of f and g multiplied by constants c1 and c2, respectively. We denote this product as c1f and c2g.

c1f(x) = c1 * f(x) = c1 * a1 on interval I1, c1 * a2 on interval I2, ..., c1 * an on interval In
c2g(x) = c2 * g(x) = c2 * b1 on interval J1, c2 * b2 on interval J2, ..., c2 * bm on interval Jm

Properties of c1f and c2g:
1. Constant on Intervals: As we can see, both c1f and c2g remain constant on each interval. This is a key feature of step functions, where the function value is constant within each interval.

2. Step Function Form: The form of c1f and c2g is consistent with the definition of a step function, as they consist of a finite number of constant segments.

Conclusion:
Based on the properties mentioned above, when multiplying two step functions f and g by constants c1 and c2, respectively, the resulting function c1f and c2g will also be a step function. Therefore, the correct answer is option 'C' (Step function).