Objective – To use tables to represent functions. A relation is a if for each input there is EXACTLY one output. function Input-Output Table (Function Table) Input and Output can also be written as an ordered pair. Input (X) Output (Y) 3 1 6 2 9 12 (X , Y) (Input, Output) (0, 3) (1, 6) (2, 9) (3, 12) Input Output

A rule or equation where there is exactly one output for every input. Function - For every x-value there is exactly one y-value. x -1 1 2 4 y -2 2 4 6 x -1 1 2 4 y 2 4 6 x 1 2 4 y -2 2 4 6 No x- value repeats No x- value repeats x-value repeats -1 1 -2 2 2 1 Yes, it is a function Yes, it is a function No, it is not a function

Determine whether the relation is a function: Input 9 25 5 3 -5 -3 2 1. (0, 2) (1, 4) (2, 6) (3, 8) 2. Output YES Each input has exactly one output!!! NO Both 9 and 25 has two different outputs! 9 25 5 2 3 -5 -3 5

Determine whether the relation is a function: 3. (-2, 4) (2, 4) (4, 2) (-2, -4) 4. (4, 5) (2, -3) (4, 9) (-2, -3) NO NO 5. 6. Input (X) Output (Y) -2 3 8 13 Input (X) Output (Y) 1 -5 2 -10 3 -15 YES YES

Complete the table using the following function rule: INPUT OUTPUT Mr. PAL Function Rule Complete the table using the following function rule: 2x + 5 = y Input Output 1 2 3 2(0) + 5 = 5 2(1) + 5 = 7 2(2) + 5 = 9 2(3) + 5 = 11

Complete the table using the following function rule: 1. y = 2x + 3 2. y = -4x + 5 Input Output 1 2 3 Input Output 1 2 3 2(0) + 3 = 3 -4(0) + 5 = 5 2(1) + 3 = 5 -4(1) + 5 = 1 -3 2(2) + 3 = 7 -4(2) + 5 = 9 -7 2(3) + 3 = -4(3) + 5 =

Input Output 1 2 3 Input Output -1 -2 -3 -3 -1 -7 4 -11 9 14 -15 3. y = 5x - 1 4. y = 4x - 3 Input Output 1 2 3 Input Output -1 -2 -3 -3 -1 4(0) - 3 = 5(0) - 1 = -7 5(1) - 1 = 4 4(-1) - 3 = -11 5(2) - 1 = 9 4(-2) - 3 = 5(3) - 1 = 14 4(-3) - 3 = -15

Objective - To graph linear equations. Graph y = 3x - 4. y x x y = 3x - 4 -3 3(-3) - 4 = -13 -2 3(-2) - 4 = -10 -1 3(-1) - 4 = -7 3(0) - 4 = -4 1 3(1) - 4 = -1 This line represents all the solutions to y = 3x - 4 2 3(2) - 4 = 2 3 3(3) - 4 = 5