Graphing Inequalities

and Functions

Major Project 2Educ220

Rachel Harrington

VocabInequalitie

s

Plotting Coordinate

s

Graphing Linear

Equations

Slope

Happy Learning!

You can go right to a lesson by clicking on one of these links, or you can just proceed by clicking next (the last button)

Audience Algebra I class

20-35 students

High School

Environment Traditional classroom

50 minutes

Diverse class

Learning Objectives1) Given a worksheet on vocabulary, student should be

able to, with 90% accuracy, correctly identify the definitions of: function, inequality, constants, coordinates, coordinate plane, graph, & negative numbers.

2) Given a calculator, computer, or graph paper, along with a worksheet of simple functions and inequalities, the student needs to graph 18 out of 20 functions/inequalities correctly.

3) Given a worksheet on solving one-step inequalities, student needs to obtain a 90% or higher through using their knowledge of the properties for inequalities.

Recall the definition…

Numbers less than zero. In graphing, numbers to the left

of zero. Negative numbers are represented by placing a minus sign (-) in front of the

number.

Recall the definition…

In math, things that do not change are called constants. The things that do

change are called variables.

Recall the definition…

A function f of a variable x is a rule that assigns to each number x in the

function's domain a single number f(x). The word "single" in this definition is very

important.

New Vocabulary:

Copy these definitions down into your notebooks

A relationship between real numbers involving inequality: x  may be greater than y,

 denoted by x > y,  or less than y,  denoted by x < y.

A unique ordered pair of numbers that identifies a point on the

coordinate plane.

The first number in the ordered pair identifies the position with regard

to the x-axis while the SECOND NUMBER identifies the position on

the Y-AXIS.

A plane with (0,0) as the origin, and two perpendicular lines that intersect at the origin, with positive and

negative direction selected on each line.

the lines are called x (drawn from left to right, with positive direction to the right of the origin) and y

(drawn from bottom to top, with positive direction upward of the origin).

Oh yes!!

A visual representation of data thatdisplays the relationship among variables,

usually cast along x and y axes.

Vertical Line Test Function ✔ NOT a function ✗

Which graphs are functions?

Simple Graphs of Inequalities

Closed circle – Also equal to.

≥ or ≤

Open circle – NOT equal to.

> or <

What do we notice about this inequality graph?

Your turn!

Answers

Your turn! Graph the inequalities:

x < 3 & x > 0

Answers

Notice how these two are the same!!

Plotting Coordinates

(x, y)

Identify these points on the graph –

(-6,-8), (-8,-4), (4,6), (7,-8), (5,-3), (5,-6)

Now using the internet!

Simple Plot Plot the coordinates of at least 10 points.

Use the (x,y) format that was

discussed.

Simple Coordinates Game

Find the x and y value for which the house is located on the coordinate plane!!

Correctly identify the location of the house at

least ten times.

Maze Game

START WITH 20 MINES IN THIS GAME.

Starting at the bottom left hand corner (near the origin!!) help the

little animal get to the target in the upper right hand corner by plotting

points he can move to without touching

the mines.

Increase the amount of mines if you can!

Graphing Linear

Equationsy = mx + b

Start with the constant also known

as “b”y = (3/2)x – 1

Then, use the “m” to plot the slope.

RISE

over

RUN

y = (3/2)x – 1

Finally, connect the dots!y = (3/2)x

– 1

Now you have your linear graph!y = (3/2)x

– 1

Your turn! Graph:

1. y = 2x + 6

2. y = x

3. y = 4x - 5

4. y = 3x

y = 2x + 6

y = x

y = 4x - 5

y = 3x

Now using the computer!

First, you need to know these two terms:

Input – the data YOU enter and want to be displayed.

Output – the date that the PROGRAM will first compute for you, and then “spit out” and show you.

Graph Sketcher

&

Graphit

Both of these interactive links are just like a graphing

calculator.

You put in a function (input) and the computer will

generate a graph of the input (giving an

output).

SlopeWhat does this do to our graph?

Slope Slider

Play with the different elements of the slope in this

activity.

See how changing different elements of an equation will affect the slope of

the linear (line) function.

Slope m = 1/3 vs. m = 3

m = 1/3 m = 3

Which equations have the steepest slope?

Graph them if you need.

y = (3/5)x – 3

y = 5x – 5

y = (1/2)x + 4

y = (4/3)x + 2

y = x – 1

In order of most steep…

1. y = 5x - 5

2. y = (4/3)x + 2

4. y = (3/5)x – 3

3. y = x - 1

5. y = (1/2)x + 4

VocabInequalitie

s

Plotting Coordinate

s

Graphing Linear

Equations Slope

As always, if you have any questions, don’t hesitate to email me!

If you need to review any of these topics, just click on

the topic!!

Email Miss. Harrington

Good job!!! Now, print out and complete these worksheets for

homework.

Graph Functions Graph Inequalities Find Slope

References http://www.shodor.org/interactivate/activities

http://www.diagram.ly/

http://www.kutasoftware.com/free.html

http://cooltext.com

http://nces.ed.gov/nceskids/createagraph/