# Notation, Composition, Inverses

# Warm-UP

There are five questions on the board. Log in to Google Classroom and answer the five questions on the Warm-Up form (Remember to look in "About")

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# Explorations

## Give Directions

Below is a map from our school to the famous Round Rock Donut Shop!

Let's write the directions from school to the Donuts shop.

Now let's write the directions back to school.

What's true about those instructions?

## Sort these cards

Open the Google Drawing

Go to ** File/Make a copy** before trying to sort the cards.

Drag the cards from the margins onto the T-Chart.

Be ready to describe what you notice about the data given.

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## Write it down

What are Inverse Functions?

An Inverse Function reverses the action of the function.

When you gave directions, you reversed them to return back to school.

In the card sort, one set of cards described the action in words - and they were reversed. In the tables, the values for x and y were reversed.

Inverse functions undo one another.

# Find the Inverse

## Three Ways to Find the Inverse

### Let's Practice Algebraically

Open the Google Drawing

Go to *File/Make a copy* before matching the answers to the problems.

Drag the answers to match the problems.

Be ready to explain your work.

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# Verifying inverses

Suppose you have two functions already.

How can you test to see if they are inverses of each other?

## Composition of functions

Composition of functions is an operation where the output from

one function becomes the input for the next function.

This is the notation ...

This is how it applies to inverses ...

Watch the video and then we will talk!

## Reflection

What did you notice in the video? What steps do you need to note?

## Let's practice

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# Mystery Time

Work with your partner to solve the attached mystery.

Make your thinking visible! Show how you determine the victim and murderer!