1. Warm up
1. Write the equation of a line with a slope of 3 and a y-intercept of ½.
2. Write the equation of a line with a slope
of -2, that passes through the point (3, -4)
1. y = 3x + ½ y = -2x + 2

2. Lesson 8-6 & 8-7 Functions
Objective: To understand what a function is and to define a function by using tables and graphs.

3. Functions
A function is a relationship between two sets; the domain and the range.
Domain is the set of all the x's in the data (x,y)
(Think of the rapper DMX - Domain Means X)
Range is the set of all the y's in the data.
In a function each domain (x) can only have 1 range (y). But each (y) can belong to more than 1 (x)
Think of this as people and birthdays - each person can only have 1 birthday, but two or more people can share the same birthday.
This can be checked by using the pencil test.

4. Pencil Test (Vertical Line Test)
For the data (1,2) (2,5) (5,7)
(-1,0)
The domain is {1,2,5,-1}
Range is {2,5,7,0}
If you were to roll the pencil
from left to right and you only roll over one point at a time, then the set is a function.

5. Functions Defined by Equations
Equations define the relationship between one set of numbers and another (typically x and y)
When talking about functions instead of y =
we can use functional notation
f(x)= is called functional notation
They can be read as “ f of x "

6. Example List the range of f(x) = 4x -3 if the domain D={0,1,2,3}
4(0) - 3 -3 1
4(1) – 3 2
4(2) - 3 5 3
4(3) - 3 9

7. Example
Given g(x) = 4x – x2, with the set of real numbers as the domain, find g(1)
g(1) = 4(1) – 12
g(1) = 4-1
g(1) = 3
Now find g(2) and g(-1)
g(2) = g(-1) = -5

8. Try: f(x) = x2 + 1
Find f( -1), f(0), f(2)
f(-1) = f(0) = f(2) = 5