For three years, a local coffee shop's rewards program offered 1 point for every whole dollar spent and additional 13 points for each purchase and 1 point for every whole dollar spent a. Write two step functions rules, f(x) and g(x) that model each rewards program. b. Describe the effect of the new points program on the corresponding graphs a. Write a function, f(x) for the original rewards program. Choose the correct answer below. A. f(x)=lceil x+8rceil B. f(x)=lfloor xrfloor +8 C. f(x)=8lceil xrceil D. f(x)=lceil xrceil +8 E. f(x)=8lfloor xrfloor F. f(x)=lfloor x+8rfloor

a. The original rewards program offers 1 point for every whole dollar spent. This can be modeled by the function $f(x) = \lfloor x \rfloor$, where $x$ represents the amount spent in dollars. The floor function, $\lfloor x \rfloor$, returns the greatest integer less than or equal to $x$, which represents the whole dollar amount spent.<br /><br />b. The new rewards program offers an additional 13 points for each purchase and 1 point for every whole dollar spent. This can be modeled by the function $g(x) = \lfloor x \rfloor + 13$, where $x$ represents the amount spent in dollars. The floor function, $\lfloor x \rfloor$, returns the greatest integer less than or equal to $x$, which represents the whole dollar amount spent. The constant 13 represents the additional points for each purchase.<br /><br />The effect of the new points program on the corresponding graphs is that the graph of $g(x)$ will be shifted upwards by 13 units compared to the graph of $f(x)$. This is because the additional 13 points for each purchase are added to the total points earned, resulting in a higher value for the same amount spent.