1 / 20

# Discovering Quadratics and Composition of Inverses - PowerPoint PPT Presentation

Discovering Quadratics and Composition of Inverses. Learning Targets. Determine how to find inverses for non-invertible functions Be able to explain what a composition of functions is Prove whether two functions are inverses of each other using algebra. Activity.

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
Download Presentation

## PowerPoint Slideshow about 'Discovering Quadratics and Composition of Inverses' - stan

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

### Discovering Quadratics and Composition of Inverses

• Determine how to find inverses for non-invertible functions

• Be able to explain what a composition of functions is

• Prove whether two functions are inverses of each other using algebra

• Each person is given a function

• You must graph it, make an x-y table and determine its inverse.

• You will then find someone who has your inverse function and compare your graph and table.

• How do you know that they are inverses of one another, state at least two pieces of evidence.

• We will do three rounds of this (7 minutes each)

• How come the quadratic can be “undone” by the square root but the original function fails the HLT?

• Based on our understanding we cannot have an inverse for this function…

…OR CAN WE?!?!?!

• Take the square root function and graph it.

• Reflect it over the line

• What do you get?

• In order to find the inverses for non-invertible functions we can use a technique that is called restricting the domain.

• By only using as our domain of the original function we can pass the HLT and create an inverse.

• Does it work both ways?

• This technique is called restricting the domain.

• This means we can actually find inverses for any function!!!!

• Lets look at the following graph and decide the inverse function…

What are the restricted domain’s?

What are the functions between these intervals?

• Find the inverses for the following functions, be sure and note what interval over each inverse occurs!

• Using these functions:

• Find the following:

• The composition of functions is inserting a function into another function

• We use the following notation when asking for the composition of two or more functions:

• When composing two or more functions the order in which we work matters!

• It’s no different than making French Fries…

• You have to cut the potato before you can fry them!!!

• You can’t fry the potato and then cut it!!!

• In other words composition of functions works like an assembly line there is only one correct direction to go!!!

• Find the inverse and then compose it with the original function

• If you take the composition of a function and its inverse you are only left with

• But what if my original function was

• Wait a second… if they are inverses of each other than the order does not matter?!?!?!

• This is quick and unique way to find out if functions are inverses of each other. If the composition does not result in then they are not inverses.

Homework:

• Worksheet

• Learned how to restrict the domain in order to find inverses for non-invertible functions

• The composition of functions

• How to use the composition of functions to find out if two functions are inverses