3.5 operations on functions
DESCRIPTION
3.5 Operations on Functions. What is a Operation? What is a Function?. Creating new Functions: Sums and Differences of Fns. Example 1: Sum and difference Functions. Creating New Functions By Products and Quotients. Example 2: Product and Quotient Functions. Caution: Find domain of f and g. - PowerPoint PPT PresentationTRANSCRIPT
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3.5 OPERATIONS ON FUNCTIONSWhat is a Operation?
What is a Function?
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CREATING NEW FUNCTIONS: SUMS AND DIFFERENCES OF FNS
EXAMPLE 1: SUM AND DIFFERENCE FUNCTIONS
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CREATING NEW FUNCTIONS BY PRODUCTS AND QUOTIENTS
EXAMPLE 2: PRODUCT AND QUOTIENT FUNCTIONS
Caution: Find domain of f and g
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COMPOSITION OF FUNCTIONS
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EXAMPLE 3: WRITING COMPOSITE FUNCTIONS AND FIND DOMAIN
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EXAMPLE 4: THE AREA OF A CIRCULAR PUDDLE
How can we determine when our little puddle will be all gone?
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3.6 INVERSE FUNCTIONS STARTER:
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3.6 INVERSE FUNCTIONS When you exchange the input and output values of a function
you get a new relation called an inverse relation. What is a relation again?? And what is a function again?? Sometimes the inverse of a function is also a function
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EXAMPLE 2: FINDING THE INVERSE FROM AN EQUATION
We now know how to find the graph of the inverse... But what about the equation
THE QUADRATIC FORMULA IS YOUR FRIEND!
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WHEN IS THE INVERSE OF A FUNCTION ALSO A FUNCTION?
Remember the Vertical Line test?
Say What?Mapping Diagrams:
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THE HORIZONTAL LINE TEST: MAKING LIFE EASY.
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*USING COMPOSITION TO DETERMINE INVERSE FUNCTIONSThis is what the inverse does:
EXAMPLE 7: VERIFYING THE INVERSE OF A FUNCTION
Add 45,47,49 to your homework!
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3.5HMWR:1,5,9,13,15,19,21,23,31,39,57 3.6HMWR:1, 9-19ODD, 31 REMEMBER TO STUDY FOR TEST NEXT CLASS 3.1, 3.2, 3.3, 3.4, 3.5, 3.6REVIEW QUS: