Chapter 1.1 Functions

Functions

Function- A function f from a set A to a set B is a relation that assigns to each element x in the set A exactly one element y in the set B.  The set A is the domain (set of inputs) of the function f, and the set B contains the range (set of outputs).

• *In some phrases, two things may seem to represent a function when they really do not. The domain must be directly correlated with the range.
• For example: Amount of time practicing basketball and your performance in a game
• This is not a function because the amount of practice time needed to do well is different for everyone
• The side length of a square and the square's area
• This is a function because the sides of a square are all the same. As the area increases, a side length increases and when area decrease a side decreases. 

Examples of Functions:

 This is a function because...

-each domain is paired with only one range.

--for every x value, there is only one y value

This is not a function because...
-1 is paired with 5 and 15.

- some x values have multiple y values

Function Notation

When an equation is used to represent a function, it is easier to name the function so that it can be referenced easily. For example, you know the equation y= 1-describes y as a function of x. If you wanted to call this function "f" then you can use function notation.

• Input: x
• Output: f(x)
• Equation: f(x) = 1 -

The symbol f(x) is read as the value of f at x or simply f of x. The symbol f(x) corresponds to the y-value for a given x. 

-f is the name of the function, f(x) is the output value of the faction at the input value

-Input is always the independent variable, output is dependent

Examples:
1. f(x)= 16-2x

• for x= -1
• f(-1)= 16-2(-1)
• =18
• for x= 4
• f(4)= 16-2(4)
• =8

2. f(x)=+  4x - 5 

• for x=1
• f(x)=1+4(1)-5
• 0

QUIZ:

1.

2.

Answers: 1. a=7, b=3, c=1.5    2. a=-24, b=-28, c=0