A company that makes dog food has determined for a bag of x pounds of dog kibble, their product lasts for S(x) servings. They use an algebraic formula that determines the number of servings in a bag as a function of the number of pounds in a bag.

Based on their current formula, a 13 pound (lb) bag will last for 18 servings. Thus we know S(13) = 18S(13)=18.

The research and development team have come up with some new formulas to improve the dog food and changes the packaging. For each case below, (i) determine where the point (13,18)(13,18) would move to on a graph of the transformed function, and (ii) write a new formula in terms of transformations (example: y = 2S(-10x+55))+20y=2S(10x+55))+20).

part a) Formula A packages 3.5 fewer pounds of dog food in the jar and lasts for 5 additional servings.

part b) Formula B packages four times as much dog food in the bag, and lasts six times as many servings as the original.

part c) Formula C packages 1/5 as much dog food in a bag, and lasts for 1/4 as many servings as the original.