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Understanding Functions and Relations: Inputs, Outputs, and Definitions

This resource provides an overview of functions and relations using examples of ordered pairs and practical applications. A function is defined as a rule that assigns exactly one output for each input, forming a relationship between two sets. The domain consists of all possible inputs (x-values), while the range includes all possible outputs (y-values). Examples are provided to illustrate the key differences between functions and non-functions, such as a soda machine versus the digestive system. Explore these concepts through interactive scenarios!

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Understanding Functions and Relations: Inputs, Outputs, and Definitions

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  1. Functions

  2. VOCABULARY: RELATION: A SET OF ORDERED PAIRS ( x , y)ex: { (-2,5) , (4,7), (8,5)}Every FUNCTION IS A RELATIONbut not every RELATION IS A FUNCTION

  3. vocabulary FUNCTION: is a rule that assigns exactly 1 output for each input. Domain: set of allpossible inputs -The x values make up the domain Range: set of all possible outputs - The y values make up the range

  4. Name That Function Inputs Frozen bagel Rye bread Cold pop-tart Frozen waffle Pumpernickel bread Outputs Toasted bagel Rye toast Hot pop-tart Toasted waffle Pumpernickel toast

  5. TOASTER!

  6. NAME THAT FUNCTION INPUT OUTPUT CLEAN SOCKS CLEAN TOWEL CLEAN SHIRT CLEAN HOODIE DIRTY SOCKS DIRTY TOWEL DIRTY SHIRT DIRTY HOODIE

  7. WASHING MACHINE!

  8. This one is not a function,Can you figure out why? x f(x)

  9. SODA MACHINE!

  10. A soda machine is NOT a function because you can get out different outputs (types of soda) when you put in the same input ( $100)

  11. SEE IF YOU CAN DETERMINE IF THIS NEXT ONE IS A FUNCTION OR NOT!

  12. Is this a Function? Inputs BIRTHDAY CAKE SANDWICH APPLE Frozen waffle RAVIOLI Outputs POOP POOP POOP POOP POOP

  13. Yes, it is a Function!DIGESTIVE SYSTEM!

  14. It is ok for a function to have the same output every time, it just can’t have different outputs for the same input.

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