Here's the problem-solving process for this:
1. Firstly, let's determine the cost of buying pizza on a regular day, represented by function f(x).
The cost of x pizzas on a regular day would be the cost of each pizza multiplied by the number of pizzas plus the delivery charge.
Therefore: f(x) = pizza_cost * x + delivery_charge
2. On Saturdays, Russo's has a 1/2 off special, so the cost of each pizza is halved.
The cost of x pizzas on a Saturday is therefore the discounted cost of each pizza multiplied by the number of pizzas plus the delivery charge.
This can be represented as an equation g(x) = discount * pizza_cost * x + delivery_charge
3. To find the transformation from f(x) to g(x), we need to express g(x) in terms of f(x).
By rearranging the equation for g(x) into a form that reflects f(x) we could get to:
g(x) = discount * f(x) + delivery_charge - delivery_charge
4. Simplifying, we find that delivery charges cancel each other out, leaving us with the transformation:
g(x) = discount * f(x)
5. In our case, the discount is half-off, so the equation of transformation from the regular day price function to the discounted Saturday price function is:
g(x) = 0.5*f(x)
This means that the Saturday price for any number of pizzas is half of what it would normally cost on any other day.