Algebra 2 Ch 3.3 Perform Function Operations and Composit ... · Algebra 2 Ch 3.3 Perform Function...

Algebra 2 Ch 3.3 Perform Function Operations and Composit.notebook

1

November 02, 2012

Oct 306:08 PM

Perform Function Operations & Composition

3.3 Perform Funcon Operaons and Composion

• Power funcons

• Add, subtract, mulply and divide funcons

• Composites of funcons

• Undefined Funcons

Oct 306:08 PM


In the past we have used functions such as f(x) and g(x), individually, but now we are going to use two functions at the same time.

With functions, we are going to :• add• subtract• multiply• divide• and do other things, such as find composites and inverses

Oct 306:08 PM


For all of the operations we are going to do today, will use the following two functions:

Oct 306:08 PM


Adding Functions

Oct 306:08 PM


Subtracting Functions

Oct 306:08 PM


Multiplying Functions


2

November 02, 2012

Oct 306:08 PM


Multiplying Functions

What value can x not be equal to?

STOP

Oct 306:08 PM


What does this mean???

We say: h of 2 equals f of g of 2.

Oct 306:08 PM


inner function

Evaluate the inner function first, which is g(x), then take your answer and use that to evaluate the outer function, which is f(x). This is called a composite function.

Oct 306:08 PM


We are still using these two functions:

So first evaluate:

Oct 306:08 PM


Now take this value and use it as the input for f(x)

Oct 306:08 PM


We want to find this answer :

But first we do this intermediate step :

Now we can evaluate the function f :


3

November 02, 2012

Oct 306:08 PM


Remember:

SO:

Oct 306:08 PM


Oct 306:08 PM


What we saw in the last example was how the domains and ranges of composite functions interact.

• The domain of a function is its inputs, which are the x values.

• The range of a function is its outputs, which are the y values ( also f(x) )

Oct 306:08 PM

Perform Function Operations & CompositionThe domain of the function g is 2.

The range of the function g is 4.

The domain of the function f is 4, and its range is 65.

Oct 306:08 PM


When we create composites, the range of the inner function, becomes the domain of the outer function.

Oct 306:08 PM


Could there have been an easier way to find the answer of a composite function?

Yes, we will find the composite equation of the two functions.

?????


4

November 02, 2012

Oct 306:08 PM


Outer Function Inner Function

Oct 306:08 PM


Oct 306:08 PM


Oct 306:08 PM


There was more work at the start of the problem, but now that we have found the composite, we can easily evaluate any value, rather than doing all of the work in the first method that we used.

Oct 306:08 PM


Now we will find

Do you think that it will be the same as ?

Oct 306:08 PM

Perform Function Operations & CompositionOuter Function Inner Function


5

November 02, 2012

Oct 306:08 PM


NOT EQUAL

Oct 306:08 PM


When we create a composite that contains a variable in the denominator, we must consider the domain, which are the input values of x.

Oct 306:08 PM


If x = 12, the value 12 is in the acceptable domain of x, so we can evaluate this function.

Oct 306:08 PM


Suppose you were going to buy a car, the dealer offers you a $2000 rebate and a 12% discount. If the sticker price of the car is $26,000, which offer would you like to apply first.

Rebate Discount

Oct 306:08 PM


Discount first, then rebate.

Rebate first, then discount.

Oct 306:08 PM

Perform Function Operations & CompositionDiscount first, then rebate.


6

November 02, 2012

Oct 306:08 PM


Rebate first, then discount.

Oct 306:08 PM


Bonus Question

At what price does it not matter if either the discount or rebate is taken first?

Oct 306:08 PM


To find the answer, set the two composites equal to each other.

There is no answer to this question!

Oct 306:08 PM


3.3 Perform Funcon Operaons and Composion

• Power funcons

• Add, subtract, mulply and divide funcons

• Composites of funcons

• Undefined Funcons

Algebra 2 Ch 3.3 Perform Function Operations and Composit ... · Algebra 2 Ch 3.3 Perform Function...

Documents

Transcript of Algebra 2 Ch 3.3 Perform Function Operations and Composit ... · Algebra 2 Ch 3.3 Perform Function...