Students will look at two functions and find the solution by scrolling up and down a table of values, graphing the intersection, then explain the meaning of the intersection and justify the solution algebraically.
Students will look at the same two functions and compare values. When is f1(x) > g1(x)? Students will also generate a data capture to compare the two functions, then create a scatter plot of the difference of the functions and draw conclusions.
Before the Activity
Students should be comfortable with function notation, solving quadratic equations, creating a scatter plot, and creating a data capture.
During the Activity
This activity is designed to have students explore individually, in pairs, or in small groups. However, an alternate approach would be to use the activity in a whole-class format. By using the computer software and the questions found on the student worksheet, you can lead an interactive class discussion.
The .tns file and the student worksheet (Solving, Comparing, and Combining Functions) guides students through the main ideas of the activity. The tns file has students find the intersection by looking at a table and by finding the intersecting points on a graph. To justify their answers, students solve the problem algerbaically. Students then find values for each function, then compare values of the two functions, determining when is f1(x) > g1(x).