Inverse Activity

 

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Inverse Functions: Day 8 Lesson Plan

 

NJCCS:

4.3.12 B. Functions

1. Understand relations and functions and select, convert flexibly among, and use various representations for them, including equations or inequalities, tables, and graphs.

Students will use equations, graphs, and numeric charts to express functions.

3. Understand and perform transformations on commonly used functions.

Students will se that the inverse of a function is a reflection of that function over the line y = x.

 

Math Content Requirements:

·        Manipulatives

ü      Students will use graphing paper to expand their understanding of what an inverse of a function is.

 

SWBAT:

·        All Students

ü      Find the inverse of a linear function by using a graphic method.

·        Some Students

ü      Find the inverse of a parabolic function given in graphing form.

·        Few Students

ü      See that the inverse of an unrestricted parabolic function is not a function.

 

Materials:

·        Graphing paper

·        Straight edge.

·        Activity instructions.

 

Motivation:

            First I will ask the class the question What does the word “inverse” mean?  The students will write down their responses and then we will discuss the question as a class. Then I will write 2/3 on the board and ask What is the multiplicative inverse of 2/3? After the students answer I will ask Why is it the inverse? Students will write down their answers to this question and then we will discuss it as a class. I expect students to know that the inverse of 2/3 is 3/2, but I want to make sure they understand that this is because when you multiply 2/3 by its inverse, 3/2, you get 1, the multiplicative identity. This activity is meant to remind them what an inverse is using an operation with which they are very familiar.

 

Procedure:

 

            Find the inverse of a linear function by using a graphing method.

 

Exploring Inverse Function Activity

            Students will be split into groups of 3 and I will hand them a handout with instruction for the activity. Then students will complete the activity. As students are working I will walk around answering questions, giving advice, keeping students on task, etc. Once there is only 10 minutes left in the period I will get everyone’s attention and then ask them what they found while they did the activity. Key things I will be looking for are:

1.)    An inverse is a reflection over the line y = x.

2.)    A function composed with its inverse is always x.

3.)    The domain of the original becomes the range of the inverse, and the range of the original becomes the domain of the inverse.

 

Once we have gone over their findings I will assign the homework and let the students continue working.

 

 

            Find the inverse of a parabolic function given in graphing form.

            See that the inverse of an unrestricted parabolic function is not a function.

                          

            Done in homework.

 

 

Homework:

            Students will complete the Exploring Inverse Functions activity if they did not do so in class. They will also find the inverse of the graph  using the same method used in class and tell whether or not it is a function.

 

 

 

Exploring Inverse Functions

Follow the steps to find the inverse of

  1. Find the y values for at least 5 values of x.
  2. Plot the points on your graph paper and draw a line through them.
  3. Switch the x and y values you found in step 1.
  4. Plot these new points on the same axis used in step 2 and draw a line through the points.
  5. Write an equation for the new line. Call this function .
  6. Fold your paper so that the two lines lie directly on top off one another.
  7. How are the two lines geometrically related?
  8. In words, f is the function that subtracts 3 from x and then divides by 2. Describe the function g in words.
  9. Predict what  and  will equal.
  10. Check your predictions.

 

Each member of the group pick a different function from the list.

                                       

  1. Complete Steps 1-5 from above to find the inverse of your function.
  2. Complete Steps 6 and 7.
  3. How can you graph the inverse of a function without finding the order pairs first?
  4. Complete Steps 8-10.
  5. How can you test to see if one function is the inverse of another?

 

First Lesson

Planned Assessment

Spaceman Spiff Lesson

General Info About Dan

Teaching Philosophy