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Algebra 2 Ch 3.3 Perform Function Operations and Composit.notebook
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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
Perform Function Operations & Composition
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
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Perform Function Operations & Composition
For all of the operations we are going to do today, will use the following two functions:
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Perform Function Operations & Composition
Adding Functions
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Subtracting Functions
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Perform Function Operations & Composition
Multiplying Functions
Algebra 2 Ch 3.3 Perform Function Operations and Composit.notebook
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Perform Function Operations & Composition
Multiplying Functions
What value can x not be equal to?
STOP
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What does this mean???
We say: h of 2 equals f of g of 2.
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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.
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We are still using these two functions:
So first evaluate:
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Now take this value and use it as the input for f(x)
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Perform Function Operations & Composition
We want to find this answer :
But first we do this intermediate step :
Now we can evaluate the function f :
Algebra 2 Ch 3.3 Perform Function Operations and Composit.notebook
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November 02, 2012
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Perform Function Operations & Composition
Remember:
SO:
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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.
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Perform Function Operations & Composition
When we create composites, the range of the inner function, becomes the domain of the outer function.
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Perform Function Operations & Composition
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.
?????
Algebra 2 Ch 3.3 Perform Function Operations and Composit.notebook
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Perform Function Operations & Composition
Outer Function Inner Function
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Perform Function Operations & Composition
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.
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Perform Function Operations & Composition
Now we will find
Do you think that it will be the same as ?
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Perform Function Operations & CompositionOuter Function Inner Function
Algebra 2 Ch 3.3 Perform Function Operations and Composit.notebook
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NOT EQUAL
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When we create a composite that contains a variable in the denominator, we must consider the domain, which are the input values of x.
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If x = 12, the value 12 is in the acceptable domain of x, so we can evaluate this function.
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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
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Perform Function Operations & Composition
Discount first, then rebate.
Rebate first, then discount.
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Perform Function Operations & CompositionDiscount first, then rebate.
Algebra 2 Ch 3.3 Perform Function Operations and Composit.notebook
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Perform Function Operations & Composition
Rebate first, then discount.
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Perform Function Operations & Composition
Bonus Question
At what price does it not matter if either the discount or rebate is taken first?
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To find the answer, set the two composites equal to each other.
There is no answer to this question!
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Perform Function Operations & Composition
3.3 Perform Funcon Operaons and Composion
• Power funcons
• Add, subtract, mulply and divide funcons
• Composites of funcons
• Undefined Funcons
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