You spent a lot of time during this unit working with linear functions. Because linear functions are easy to work with, we often use them as mathematical models to represent real-world situations. In reality, many of these situations are not exactly linear and the mathematical models we create are only approximations. It is important to be able to recognize whether or not it is reasonable to use a linear function to approximate the increase (or decrease) of something as a function of something else.
For which of the following situations would a linear function be a reasonable choice for a mathematical model?
Explain your choices.
The success rate of field-goal kicking as a function of distance from the goal post
The number of people who have heard something as a function of time after the first person is told
Stopping distance (in a car) as a function of speed
You have learned about representing functions with graphs, words, tables of numbers, and with algebraic formulas. Do you have a preference for one or more of these four ways of working with functions? Explain to your classmates why you have this preference or why it doesn't matter to you which representation you use.
What questions do you still have about the unit? Ask them here and you classmates may give you the answers you seek.