Section 4.1 Coordinate Plane Section 4.2 Graphing Functions

On the first day of school, I created a seating chart for my classes On the first day of school, I created a seating chart for my classes. I created 5 rows of desks with 6 desks in each row. Someone sits in the third row at the second desk (3,2) and someone sits in the second row at the third desk (2,3). Are these seats the same? No!! The seats (3,2) and (2,3) are called ordered pairs because the order in which the pair of numbers is written is important!!

Who is sitting in desk (4,2)? A B C D E 3 F G H I J K L M N O 2 P Q R S T 1 1 2 3 4 5

Ordered pairs are used to locate points in a coordinate plane. y-axis (goes up and down) 5 -5 5 x-axis (goes left to right) -5 origin (0,0)

In an ordered pair, the first number is the x-coordinate In an ordered pair, the first number is the x-coordinate. The second number is the y-coordinate. Graph. (-3, 2) 5 • 5 -5 -5

What is the ordered pair for A? 5 (3, 1) (1, 3) (-3, 1) (3, -1) • A -5 5 -5

What is the ordered pair for B? (3, 2) (-2, 3) (-3, -2) (3, -2) 5 -5 5 • B -5

What is the ordered pair for C? (0, -4) (-4, 0) (0, 4) (4, 0) 5 -5 5 • C -5

What is the ordered pair for D? (-1, -6) (-6, -1) (-6, 1) (6, -1) 5 -5 5 • D -5

II (-, +) I (+, +) III (-, -) IV (+, -) The x-axis and y-axis separate the coordinate plane into four regions, called quadrants. II (-, +) I (+, +) III (-, -) IV (+, -)

Name the quadrant in which each point is located (-5, 4) II III IV None – x-axis None – y-axis

Name the quadrant in which each point is located (-2, -7) II III IV None – x-axis None – y-axis

Name the quadrant in which each point is located (0, 3) II III IV None – x-axis None – y-axis

Functions A function is a relation in which each element of the domain is paired with exactly one element of the range. Another way of saying it is that there is one and only one output (y) with each input (x). f(x) y x

Function Notation Input Name of Function Output

Determine whether the relation is a function. 1. {(2, 3), (3, 0), (5, 2), (4, 3)} YES, every domain is different! f(x) 5 2 f(x) 2 3 f(x) 3 f(x) 4 3

Determine whether the relation is a function. 2. {(4, 1), (5, 2), (5, 3), (6, 6), (1, 9)} f(x) 4 1 f(x) 5 2 NO, 5 is paired with 2 numbers! f(x) 5 3 f(x) 6 f(x) 1 9

Is this relation a function? {(1,3), (2,3), (3,3)} Yes No Answer Now

Vertical Line Test (pencil test) If any vertical line passes through more than one point of the graph, then that relation is not a function. Are these functions? FUNCTION! FUNCTION! NOPE!

Vertical Line Test FUNCTION! NO! NO WAY! FUNCTION!

Is this a graph of a function? Yes No Answer Now

3(3)-2 7 3 -2 -8 3(-2)-2 Given f(x) = 3x - 2, find: = 7 1) f(3) 2) f(-2) 3(3)-2 7 3 = -8 3(-2)-2 -2 -8

Given h(z) = z2 - 4z + 9, find h(-3) (-3)2-4(-3)+9 -3 30 9 + 12 + 9 h(-3) = 30

Given g(x) = x2 – 2, find g(4) 2 6 14 18 Answer Now

Given f(x) = 2x + 1, find -4[f(3) – f(1)] -40 -16 -8 4 Answer Now

Making an Input-Output Table When given an equation, you can make an input-output table to determine if it is a true function or not Example:

Is a function? Make an input-output table. Usually, it is easier to use -2, 0, 1, and 2 as the DOMAIN x y -2 1 2

Make an input-output table to determine if this is a function

Homework: Worksheet 11. 3 Functions & 11 Homework: Worksheet 11.3 Functions & 11.2 Determining Domain and Range of Functions.