An Introduction to Functions

1
Section 2.3

• An Introduction to Functions

2
Whats your Function?

• A function is a SPECIAL type of relation.
• Vending Machine
• We want a particular candy to come out when we
  press a particular button.
• Ie, one OUTPUT for each INPUT.
• Each input (x) corresponds to exactly one output
  (y).

3
Examples Is it a function? Give Domain and
range, too.

• (-1,1),(0,0),(1,-1)
• (-2,6),(-3,1),(4,5),(-3,-1)

4
Function basics

• Two different inputs can give the same output.
• We are fine with 2 buttons on the vending machine
  giving out Hershey Bars
• But, two different outputs cannot result from the
  same input.
• We dont want to randomly end up with a Snickers
  OR KitKat if we press Button B.
• Note Pg. 160 Work Smart at bottom of page is
  WRONG!

5
What about graphs?

• A function can have only one y value for each x.
• So, a graph cannot be a function if two points
  with the same X have different Ys.
• Easiest way to tell
• The Vertical Line Test
• If you can draw a vertical line through the graph
  and have it intersect the graph in more than one
  place, it is NOT a function.

6
Graphs Functions?
7
More
8
More
9
Function Notation

• Functions have their own special notation.
• Denoted by letters f,g,F, G, etc.
• f(x) means function of x
• So, instead of writing
• y 2x3
• We write
• f(x) 2x3 this way, we are told that it is a
  function

10
Find the value of a function

• F(x)2x2-x
• What is
• F(2)?
• F(-3)?
• Whatever is in the ( ) is the input into the
  function. Replace every occurance of the IV with
  that value!

11
More finding values

• What is
• f(-x)?
• f(2a)?
• f(x4)?

12
Graphing a function

• The graph of a function is the set of ALL ordered
  pairs (x,y) such that y f(x).
• How?
• Plot points, as we did before
• Connect the dots

13
Functions in Word Problems

• The number N of cars produced at a certain
  factory in 1 day after t hours is given by
• where 0lt t lt10
• Identify the DV and IV
• Evaluate N(4). What does that mean in terms of
  the problem?