Graphing Inequalities and Functions Major Project 2 Educ220 Rachel Harrington.
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Transcript of Graphing Inequalities and Functions Major Project 2 Educ220 Rachel Harrington.
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/