In this lesson, students explore how to create new functions by combining two functions through adding, subtracting, multiplying, or dividing. Students start by considering the functions defining total number of books sold and total US population from 2010 to 2016. They then calculate the numerical value of the function defined by their quotient to consider the number of books sold per person, working with one aspect of modeling with functions. Students then focus on the graphs of two functions without context and use the numerical information related by a graph to sketch a new function defined by the sum of the two original functions.
During these activities, students are asked to do the same type of calculation several times, for different pairs of functions in order to help make the connection between the numerical values of the original functions and the numerical value of the new function that was created by adding, subtracting, multiplying, or dividing them (MP8).
- Create new functions by adding, subtracting, multiplying, and dividing simpler functions with and without context.
- Let’s make some new functions using other functions.
- I can combine two functions in different ways.