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 2. y = -2x + 2

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

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.

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.

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 "

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

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) = 4 g(-1) = -5

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