Phoebe spends her weekends competing in chess matches. so far, she has won 10 out of 20 matches that she has played. she wants to improve her winning percentage to 80% and needs to calculate how many consecutive matches she must win to meet her goal. phoebe decides to model her situation using a rational function, g(x), where x is the number of consecutive matches she must win.
b1: quadratic
b2: exponential
b3: rational
b4: linear

a1: yes, phoebe chose the most appropriate function type for her model. the situation describes a ratio of two expressions involving x. since rational functions include the ratio of two polynomials, phoebe was correct to choose a rational function to model her situation.
a2: yes, phoebe chose the most appropriate function type for her model. all problems involving rates and percentages should be modeled with rational functions.
a3: no, phoebe did not choose the most appropriate function type for her model. although the situation is describing a ratio, this does not necessarily mean that the model must be rational.
a4: no, phoebe did not choose the most appropriate function type for her model. she wants to know the difference between two values, so a rational model is not appropriate.