3.5 Operations on Functions

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Presentation transcript:

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

Composition of Functions

Example 3: Writing Composite Functions and Find Domain

Example 4: The Area of a Circular Puddle How can we determine when our little puddle will be all gone?

3.6 Inverse Functions Starter:

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

Example 2: Finding the Inverse from an Equation We now know how to find the graph of the inverse... But what about the equation Example 2: Finding the Inverse from an Equation The quadratic formula is your friend!

When is the inverse of a function also a function? Say What? Mapping Diagrams: Remember the Vertical Line test?

The Horizontal Line Test: Making life easy.

*Using Composition to Determine Inverse Functions This is what the inverse does: Example 7: Verifying The Inverse of a Function Add 45,47,49 to your homework!

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, 3.6 Review Qus: