INTRODUCTION TO FUNCTIONS2006 by Kelly Howarth
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.
Heres an example of a function. Our Input numbers will be xs and our Output results will be ys.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?
We can make a table for our Input values and our Output values. Lets call this an x-y table.
y (Outputs)-4x + 2(Relation)X (Inputs)
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!
Math Definition of a RelationIn math, if we have one x input that has MORE THAN ONE y output, then we have a relation. Heres what we mean.
Specifically, if we have several ys for the same x, then we have a relation. Here is a picture next. . .
We are MARRIED! She is the ONE LOVE of my life!! We have a relationship that functions very well!!He is sooo Hot! Heres a hot math definition for you next!
Definition of a Function: A function is a relation in so that every Input value (xs) have ONLY ONE output value (ys). Or. . .For every x, there is ONLY ONE y.Here is an example of a function;
So, if he tried to have relationships with other women after we are married, then he wont 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.
And just as a guy can carry on several relationships while dating (as long as he doesnt get caught!); Mathematically, if one x (input number) has SEVERAL ys (output numbers), then we have a RELATION. A RELATION is like dating.
Function notationSo, why would I want to write f(x) instead of y if they mean the same thing? Thats just MORE WORK!
Heres why you might want to use the function notation f ( x ) instead of merely writing y. Watch this closely!
I can use a function to figure out how far I will travel if I crawl at 3 miles per hour! Watch this!
Function examples. . .
Evaluate the following functions