DISCOVERING QUADRATICS AND COMPOSITION OF INVERSES.

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Presentation transcript:

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 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)

QUADRATICS… 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?!?!?!

QUADRATICS…

RESTRICTING THE DOMAIN

This means we can actually find inverses for any function!!!! Lets look at the following graph and decide the inverse function…

HOW WOULD WE WRITE THE INVERSES FOR THIS FUNCTION What are the restricted domain’s?

HOW WOULD WE WRITE THE INVERSES FOR THIS FUNCTION What are the functions between these intervals?

PIECEWISE FUNCTION TABLE Restricted DomainFunctionInverse

HOW WOULD WE WRITE THE INVERSES FOR THIS FUNCTION

YOU TRY RESTRICTING THE DOMAIN

COMPOSITION OF FUNCTIONS

ORDER MATTERS!!! 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!!!

THAT’S COOL, BUT WHAT DOES IT HAVE TO DO WITH INVERSES?

INVERSE COMPOSITION

DETERMINE IF THE FOLLOWING FUNCTIONS ARE INVERSES

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 What we did:Homework: