Burst the Inverse!

Learning Resource Type

Lesson Plan

Subject Area



9, 10, 11, 12


This lesson allows students to investigate functions and their inverses by hand and using graphing calculators.  Students will also use equations and graphs.  Students will collaborate to develop and justify ideas/conjectures about functions and inverses.

Mathematics (2019) Grade(s): 09-12 - Algebra II with Statistics


Solve simple equations involving exponential, radical, logarithmic, and trigonometric functions using inverse functions.



  • Radical equations
  • Exponential equations
  • Logarithmic equations
  • Trigonometric equations
  • Inverse functions


Students know:

  • Techniques for rewriting algebraic expressions using properties of equality.
  • Methods for solving exponential, logarithmic, radical, and trigonometric equations.


Students are able to:

  • Accurately use properties of inverse to rewrite and solve an exponential, logarithmic, radical, or trigonometric equation.
  • Use technology to approximate solutions to equation, if necessary.


Students understand that:

  • The inverse of exponential, logarithmic, radical, and trigonometric functions may be used to aid in the solution of problems.


  1. Solve simple equations involving exponential, radical, logarithmic, and trigonometric functions using inverse functions.

Primary Learning Objectives

Students will discover and use the properties of functions and their inverses.  Students will find inverse equations of linear functions given other linear function equations.   Students will use slope criteria and formulas to solve problems and justify reasoning for developed discoveries.

Additional Learning Objective(s)

Students will work cooperatively to discover patterns in the graph table of values while problem solving. Students will verify conclusions by finding slope, developing equations and graphing both functions on the same axes.  Students can manually or use graphing calculators to complete the tasks.  



As students enter the classroom, they should be given a group indicator that tells them where to sit. Inform the students that their mission will be to determine the inverse of linear functions.  


1.  Student groups should develop a table of values for each linear function assigned, reverse the coordinates, find the slope of this set of coordinates, develop equations for the coordinate sets, and graph both equations on the same axes.  They should record these findings on their own paper (this information can be keyed into their graphing calculators). 

2.  The students should come back to the classroom and key their information into their graphing calculators (using the list key on the graphing calculator) to determine the slopes and equations.  They should look for patterns of symmetry in graphs.  The groups must agree on findings and be able to justify them. 

3. For students who are unable to find slopes and understand function inverses, provide necessary feedback to move them forward with their thinking.  Refer to Slope (Rise over Run): https://www.youtube.com/watch?v=zTa0xTu9Yv4.

Refer to: 




1.  The teacher should be sure that students are using graphing tables and slopes correctly to develop equations.

2.  Groups will discuss properties discovered and begin justifying their ideas as well as creating equations and graphs to match their tables in the calculator.

3.  Allow students the time to prepare attractive posters to share with the class to begin discussions about Inverse functions and tables, along with having the groups share their findings using the Smartview function of the calculator.


Use the provided rubric to assess student work individually and as a group. Students should justify all the reasoning stated on the poster.  The Assessment Process is ongoing. The teacher should visit each group and ask questions to make sure students apply the properties of functions and their inverses.  Display the posters in the classroom and have students present conclusions. As students present posters and graphing calculator findings, they should compare posters for other information not listed on their group's poster.

Assessment Strategies

Use the rubric to continuously assess student work individually and as a group.  The teacher should visit each group and ask questions to make sure students apply the properties of functions and their inverses.  


Extensions can be to include understanding the process for algebraically finding inverses of functions and why the process works.  Also, Does the process work for quadratic and higher functions? Justify the reasoning!


Total Duration

61 to 90 Minutes



  • Have loose leaf graph paper and chart paper available to be used for lesson.
  • Have graphing calculator ready to be assigned.


  • Algebra students should be able to graph coordinates on Cartesian plane and find Slopes of lines.
  • Students should be able to use slope intercept form to solve problems and have some knowledge of using the graphing calculators.

Materials and Resources

Poster Paper or Poster with grid lines, sticky notes of different types, straight edge, markers, and loose leaf graph paper, student may use their own devices or teacher-issued graphing calculators.

Technology Resources Needed

Computer with Internet access, LCD Projector and Document camera to share student paper or calculator work (helpful but not necessary). 

Approved Date