Warm Up 1/4/15 Turn to a neighbor and tell them about a fun experience you had over break. Be prepared to share with the class!

Objective The students will be able to: graph ordered pairs on a coordinate plane.

ordered pair – a pair of numbers used to locate a point on a coordinate plane. coordinate plane – a plane formed by the intersection of a horizontal number line called the x-axis and a vertical line called the y-axis. x-axis – the horizontal axis on a coordinate plane. y-axis – the vertical axis on a coordinate plane. x-coordinate – the first number in an ordered pair; it tells the units to move right or left from the origin. y-coordinate – the second number in an ordered pair; it tells the units to move up or down from the origin. origin – the point where the x-axis and the y-axis intersect on the coordinate plane.

The Cartesian Coordinate Plane -The Cartesian plane was the brainchild of French mathematician Rene Descartes trying to combine algebra and geometry together. -Descartes took a second number line and standing it on end, crossed the lines at zero to form a grid like pattern. -The number lines when drawn like this, are called “axes”. The horizontal line is called the “x-axis”; the vertical line is called the “y- axis”.

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

Ordered pairs are used to locate points in a coordinate plane. x-axis (horizontal axis) origin (0,0) y-axis (vertical axis)

y x Graphing an ordered pair, (point): (x, y) Graph point A at (4, 3) The first number, 4, is called the ___________. x-coordinate It tells the number of units the point lies to the __________ of the origin. The second number, 3, is called the ___________. y-coordinate It tells the number of units the point lies _____________ the origin. left or right above or below (4, 3)

y x Graphing an ordered pair, (point): (x, y) Graph point B at (2, –3) The first number, 2, is called the ___________. x-coordinate It tells the number of units the point lies to the __________ of the origin. The second number, –3, is called the ___________. y-coordinate It tells the number of units the point lies _____________ the origin. left or right above or below (2, – 3)

What is the ordered pair for A? 1.(3, 1) 2.(1, 3) 3.(-3, 1) 4.(3, -1) A

What is the ordered pair for B? 1.(3, 2) 2.(-2, 3) 3.(-3, -2) 4.(3, -2) B

What is the ordered pair for C? 1.(0, -4) 2.(-4, 0) 3.(0, 4) 4.(4, 0) C

What is the ordered pair for D? 1.(-1, -6) 2.(-6, -1) 3.(-6, 1) 4.(6, -1) D

Write the ordered pairs that name points A, B, C, and D. A = (1, 3) B = (3, -2) C = (0, -4) D = (-6, -1) A B C D

Name the quadrant in which each point is located (-5, 4) 1.I 2.II 3.III 4.IV 5.None – x-axis 6.None – y-axis

Name the quadrant in which each point is located (-2, -7) 1.I 2.II 3.III 4.IV 5.None – x-axis 6.None – y-axis

Name the quadrant in which each point is located (0, 3) 1.I 2.II 3.III 4.IV 5.None – x-axis 6.None – y-axis

Warm Up 1/5/15 Solve the following rebus puzzles

Graphing an Equation Using ordered pairs

Generate ordered pairs for the equation y = x + 3 for x = –2, –1, 0, 1, and 2. Graph the ordered pairs. Xy

Complete the table of values to determine the ordered pairs. Graph the equation on a coordinate plane.

XY

XY

When graphing, you always want to draw neatly.

Cartography, the science of map making, is an application of graphing on a coordinate plane. Cartographers map a region of the surface of the earth onto part of a plane.

Warm Up 1/6/15 Moving or not?

Definition: A relation is any set of ordered pairs. A={(1,3),(2,4),(3,5)}

A relation can also be represented by: a table of values, a graph, a mapping diagram, and an equation (equations come later).

Domain: In a set of ordered pairs, (x, y), the domain is the set of all x-coordinates. Range: In a set of ordered pairs, (x, y), the range is the set of all y-coordinates.

Given the following set of ordered pairs, find the domain and range. Ex:{(2,3),(-1,0),(2,-5),(0,-3)} Domain: {-1,0,2} Range:{-5,-3,0,3} If a number occurs more than once, you do not need to list it more than one time.

Practice: Find the domain and range of the following set of ordered pairs. 1. {(3,7),(-3,7),(7,-2),(-8,-5),(0,-1)} Domain:{-8,-3,0,3,7} Range:{-5,-2,-1,7}

xy State the domain and range of the following Relation (represented by a mapping diagram)

xy State the domain and range of the following relation.

Give the domain and range for the following relation. The domain value is all x-values from 1 through 5, inclusive. The range value is all y-values from 3 through 4, inclusive. Domain: 1 ≤ x ≤ 5 Range: 3 ≤ y ≤ 4 ^^This is known as interval notation^^

D: –5 ≤ x ≤ 3 R: –2 ≤ y ≤ 1 Give the domain and range for the following relation.

D: R:

Give the domain and range for the following relation. D: R:

Warm Up 1/7/15 /watch?v=vJG698U2Mvo

Functions A relation is a function provided there is exactly one output for each input. A relation is NOT a function if at least one input has more than one output

INPUT (DOMAIN) OUTPUT (RANGE) FUNCTION MACHINE In order for a relationship to be a function… EVERY INPUT MUST HAVE AN OUTPUT TWO DIFFERENT INPUTS CAN HAVE THE SAME OUTPUT Functions ONE INPUT CAN HAVE ONLY ONE OUTPUT

No two ordered pairs can have the same first coordinate (and different second coordinates). Which of the following relations are functions? R= {(9,10, (-5, -2), (2, -1), (3, -9)} S= {(6, a), (8, f), (6, b), (-2, p)} T= {(z, 7), (y, -5), (r, 7) (z, 0), (k, 0)}

Identify the Domain and Range. Then tell if the relation is a function. Input Output Domain = {-3, 1,3,4} Range = {3,1,-2} Function? Yes: each input is mapped onto exactly one output

Input Output Identify the Domain and Range. Then tell if the relation is a function. Domain = {-3, 1,4} Range = {3,-2,1,4} Function? No: input 1 is mapped onto Both -2 & 1 Notice the set notation!!!

xy xy xy Relation (not a function) Function State whether or not the following relations are functions or not.

xy xy xy function Relation (not a function) State whether or not the following relations are functions or not.

1. {(2,5), (3,8), (4,6), (7, 20)} 2. {(1,4), (1,5), (2,3), (9, 28)} 3. {(1,0), (4,0), (9,0), (21, 0)}

The Vertical Line Test If it is possible for a vertical line to intersect a graph at more than one point, then the graph is NOT the graph of a function.

(-3,3) (4,4) (1,1) (1,-2) Use the vertical line test to visually check if the relation is a function. Function? No, Two points are on The same vertical line.

(-3,3) (4,-2) (1,1) (3,1) Use the vertical line test to visually check if the relation is a function. Function? Yes, no two points are on the same vertical line

Examples I’m going to show you a series of graphs. Determine whether or not these graphs are functions. You do not need to draw the graphs in your notes.

#1 Function?

#2

Function? #3

Function? #4

#5 Function?

#6

#7 Function?

#8

Warm Up 1/8/15 Why don’t you ever see hippopotamus hiding in trees? Because they’re good at it.

What time is it when you go to the dentist? Tooth-hurty.

What do you call a big pile of kittens? A meowntain.

Graphing Relationships Graphs can be used to illustrate many different situations. For example, trends shown on a cardiograph can help a doctor see how a patient’s heart is functioning. To relate a graph to a given situation, use key words in the description.

Example 1: Relating Graphs to Situations Each day several leaves fall from a tree. One day a gust of wind blows off many leaves. Eventually, there are no more leaves on the tree. Choose the graph that best represents the situation. Step 1 Read the graphs from left to right to show time passing.

Check It Out! Example 1 The air temperature increased steadily for several hours and then remained constant. At the end of the day, the temperature increased slightly before dropping sharply. Choose the graph that best represents this situation. Step 1 Read the graphs from left to right to show time passing.

As seen in Example 1, some graphs are connected lines or curves called continuous graphs. Some graphs are only distinct points. They are called discrete graphs The graph on theme park attendance is an example of a discrete graph. It consists of distinct points because each year is distinct and people are counted in whole numbers only. The values between whole numbers are not included, since they have no meaning for the situation.

Example 2B: Sketching Graphs for Situations Sketch a graph for the situation. Tell whether the graph is continuous or discrete. A small bookstore sold between 5 and 8 books each day for 7 days. The graph is discrete. The number of books sold (y-axis) varies for each day (x-axis). Since the bookstore can only sell whole numbers of books, the graph is 7 distinct points.

Check It Out! Example 2a Sketch a graph for the situation. Tell whether the graph is continuous or discrete. Jamie is taking an 8-week keyboarding class. At the end of each week, she takes a test to find the number of words she can type per minute. She improves each week. The graph is discrete. Each week (x-axis) her typing speed is measured. She gets a separate score (y-axis) for each test. Since each test score is a whole number, the graph consists of 8 distinct points.

Sketch a graph for the situation. Tell whether the graph is continuous or discrete. Check It Out! Example 2b Henry begins to drain a water tank by opening a valve. Then he opens another valve. Then he closes the first valve. He leaves the second valve open until the tank is empty. As time passes while draining the tank (moving left to right along the x-axis) the water level (y-axis) does the following: initially declines decline more rapidly and then the decline slows down. The graph is continuous.

Lesson Quiz: Part I 1. Write a possible situation for the given graph. Possible Situation: The level of water in a bucket stays constant. A steady rain raises the level. The rain slows down. Someone dumps the bucket.

2. A pet store is selling puppies for $50 each. It has 8 puppies to sell. Sketch a graph for this situation. Lesson Quiz: Part II