Linear Functions

 

 


 
Linear Functions

Students will analyze functions by investigating rates of change, intercepts, and zeros.

 Stacking Cups

Teacher and study PDF forms available

Study of linear equations, giving physical significance to slope and y-intercept

 

 Bungee Jumping With a Toy Doll

Students determine the length of a bungee cord made of rubber bands that will allow a toy doll to fall as close as possible to the ground without hitting it. Teams of students collect data and graph these data, determine a trend line and its equation, and extrapolate to the desired distance the doll is to fall. Activity sheets, a solution to the problem, and links to the NCTM site that inspired the problem are included.

 

Money Investigation 3

Teacher and study PDF forms available

Introduction to the coordinate axis, including plotting points, writing linear functions algebraically, relating slope and y-intercept to context

 

Talk Is Cheap

This task can be used to introduce students to functions in a realistic setting—choosing a cell phone plan given certain conditions. Students gain experience working with decimals and translating among different representations of linear functions. They use the graphing calculator to find the intersection of two linear functions graphically and interpret the intersection in terms of the problem situation.

 

You’re Toast, Dude!

Students extend their understanding of functions to rational functions by exploring average cost. They gain experience in moving between a problem context and its mathematical model in order to solve problems and make decisions.

 

Autobahn

This task allows the student to use calculations with rational numbers to compute average speeds.

 

Genetic Factors: Effects on Medication

Teacher and study PDF forms available

Purpose is to study a function (y = k/x) and to interpret its graph in context; in particular, students study the meaning of asymptote. Uses fact that elimination rate for some drugs varies by population.