Final answer:
A fitted function can model the relationship between variables, allowing for computation and plotting of data pairs. It can also predict future values and make problem-solving easier by using distributions like the probability distribution function.
Step-by-step explanation:
A function fitted to data can be used to solve problems by modeling the relationship between variables. When the function that describes the dependence of y on x is known, it enables the computation of x,y data pairs that can be plotted to offer visual insights and to predict values. This graphical method is particularly useful, allowing for the estimation of variables to a high degree of accuracy, typically to three digits.
Furthermore, in the context of probability, a probability distribution function acts as a pattern to simplify complex probability problems by leveraging the distribution's special characteristics to make calculations easier.
For instance, using the least-squares line to estimate future values, such as predicting the gold medal time for the next Summer Olympics, illustrates how fitting a line to data can be a powerful tool for making reasonable and substantiated predictions.
Essentially, fitted functions can streamline problem-solving by providing a structured approach to analyze and make inferences from data, which is a process otherwise known as Work It Out in many educational programs. This approach takes students through analytical or computational problems step by step to derive their solutions.