Graphing and Functions

Graphing

Goals:

• Understand the coordinate plane

• Graph ordered pairs

• Identify functions from a set of ordered pairs.

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Vocabulary

coordinate plane, axes, origin, quadrants, order pair, x-coordinate, y-coordinate

Let's define some terms

coordinate plane: composed of the x-axis (horizontal) and y-axis (vertical)

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Origin: the point where the x-axis and y-axis meet --> (0,0)

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Quadrants: The 4 sections the plane is broken into

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​Origin

​QUADRANT

I​

​QUADRANT

I​I

​QUADRANT

I​II

​QUADRANT

IV​

Let's define some terms

Ordered pair: follows the format (x,y) and used for graphing

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x: the x-coordinate in the ordered pair. Moves left (negative) or right (positive)

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y: the y-coordinate in the ordered pair. Moves up (positive) or down (negative).

Write the order pairs for the given points

Point A

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Point B

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Point C

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Point D​

​Graph the following ordered pairs. Don't forget that ALL ordered pairs ALWAYS follow the format (x,y)

(3,7)

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​(-5,2)

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​(-5,-5)

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​(0,7)

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​(8,0)

Now let's talk about functions

A function is a process or a relation that associates each element "x" of a set to a single element "y" of another set "y." These x- and y-values are also called inputs and outputs respectively.

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Every x-value (aka inputs) are connected to one y-value (aka outputs).

​Take a look at these examples.

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One set of points represents a function while the other does not.

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Can you tell which one is the function?​

​Set A:

{(10,9), (-2,-16), (-6,7), (5,8), (8,-16), (-11,9)}​

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​Set B

​{(-7,4), (-8,3), (-7,7), (-20,8), (5,9), (3,1), (2,6)}

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​Set A. . . IS a function

{(10,9), (-2,-16), (-6,7), (5,8), (8,-16), (-11,9)}​

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Every input (x-value) in set A matches to exactly 1 output (y-value).

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​Set B. . . IS NOT a function

​{(-7,4), (-8,3), (-7,7), (-20,8), (5,9), (3,1), (2,6)}

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There was one input (x-value) that repeated AND had different outputs (y-values) even though they had the same input. ​

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​EXAMPLE OF FUNCTION

EXAMPLE OF NOT A FUNCTION

Practice with IXL

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• ​Objects on a coordinate plane:  https://www.ixl.com/math/grade-6/objects-on-a-coordinate-plane?signInRedirect=https%3A%2F%2Fwww.ixl.com%2Fsignin%2Fhse

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• Coordinate Plane Review: https://www.ixl.com/math/geometry/coordinate-plane-review?signInRedirect=https%3A%2F%2Fwww.ixl.com%2Fsignin%2Fhse

Day 2: ​

So what are functions again?

• a process or a relation that associates each element "x" of a set (aka the domain) to a single element "y" of another set "y" (aka range)

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• Functions can be defined by a set of ordered pairs, a table and even an equation!

We'll be looking at tables and equations a little closer

• Use a tables to sort out your x- and y-values

• Left column are the x-values

• Right column are the y-values

​inputs (x-values)	​outputs (y-values)
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Let's start with: f(x)=2x+5

​inputs (x-values)	​outputs (y-values)
​-2	​
-1​	​
0​	​
1​	​
​2	​

​Step 1: choose values for x. Recommended:-1,0,1

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Step 2: substitute the value of x into the equation (aka the "rule") every time you see an x being used.

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Step 3: the result you get from Step 2 is your output.​

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NOTE: These steps are useful when you are being asked to graph an equation! From the equation you can create a table and from the table you can create ordered pairs that you can plot on a coordinate plane to give you the graph.

f(x) = ___________

​inputs (x-values)	​outputs (y-values)
​-2	​
-1​	​
0​	​
1​	​
​2	​

​Step 1: choose values for x. Recommended:-1,0,1

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Step 2: substitute the value of x into the equation (aka the "rule") every time you see an x being used.

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Step 3: the result you get from Step 2 is your output.​

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NOTE: These steps are useful when you are being asked to graph an equation! From the equation you can create a table and from the table you can create ordered pairs that you can plot on a coordinate plane to give you the graph.

Day 3: Function Graphs​

​Some text here about the topic of discussion.

VERTICAL LINE TEST:

The process where we use a vertical straight line to check if it intersects with the given graph are more than just one point.

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Crossing at only 1 point --> Function

Crossing at 2 points or more --> Not a Function​

How can we tell if a graph represents a function?

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Day 4: Equations from Tables​

​Tables from Equations

f(x) = _______

x is the input

f(x) is the out​

Some text here about the topic of discussion

​x	​f(x)
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