Warm up

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 2. 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} • R = {-3,1,5,9}

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) = 4 g(-1) = -5

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