1. INTRODUCTION TO FUNCTIONS ©2006 by Kelly Howarth

2. What is a function? “A function is like an “input-output” machine. The machine RELATES the number we Input in a certain way to the Output.

3. “Here’s an example of a function. Our Input numbers will be x’s and our Output results will be y’s. “Here, we see that whatever number we replace the variable x with gets doubled, then 3 is subtracted from that product. The resulting number is y. So, if we choose an input value (x value) of 2, what is our output value (y value) ? “Seems to me that we could DECIDE to choose substitute ANY NUMBER for x. How about if we see what happens if we choose a few different numbers?”

4. “We can make a table for our Input values and our Output values. Let’s call this an x-y table. y (Outputs) -4x + 2 (Relation) X (Inputs)

5. “OOPS! Uh,...er...Caught us kissing! Well, anyway, it is OBVIOUS that we enjoy a RELATIONSHIP!” “I enjoy several relationships since I date several girls at the same time! Heh! Heh! ” “YOU CAD! You, one guy, are trying to date several girls at the same time!”

6. Math Definition of a Relation In math, if we have one x input that has MORE THAN ONE y output, then we have a relation. Here’s what we mean.In math, if we have one x input that has MORE THAN ONE y output, then we have a relation. Here’s what we mean. Specifically, if we have several y’s for the same x, then we have a relation. Here is a picture next...Specifically, if we have several y’s for the same x, then we have a relation. Here is a picture next...

8. “We are MARRIED! She is the ONE LOVE of my life!! We have a relationship that functions very well!!” “He is sooo Hot! Here’s a hot math definition for you next!”

9. Definition of a Function: A function is a relation in so that every Input value (x’s) have ONLY ONE output value (y’s).A function is a relation in so that every Input value (x’s) have ONLY ONE output value (y’s). Or...Or... For every x, there is ONLY ONE y.For every x, there is ONLY ONE y. Here is an example of a function;Here is an example of a function;

11. “So, if he tried to have relationships with other women after we are married, then he won’t function! “So, just like a marriage is ONE man with only ONE woman; in a math function, each x has only one y. Each input number has only one output number. A function is like marriage.”

12. “And just as a guy can carry on several relationships while dating (as long as he doesn’t get caught!); Mathematically, if one x (input number) has SEVERAL y’s (output numbers), then we have a RELATION. A RELATION is like dating.”

13. Function notation “So, why would I want to write f(x) instead of y if they mean the same thing? That’s just MORE WORK!”

14. “Here’s why you might want to use the “function notation” f ( x ) instead of merely writing y. Watch this closely!”

15. “I can use a function to figure out how far I will travel if I crawl at 3 miles per hour! Watch this!”

16. Function examples...

17. Evaluate the following functions

18. Assignment: