Input and Output Math

Relation and Function

Advance Algebra Math 10A

Intended Learning Outcomes:

​At the end of the session, the learners should have:

Advance Algebra Math 10A

​🔷 determined the relationship between input and output

​🔷​ determined dependent and independent variables

​🔷 solved for the value of the input and output

​🔷 enumerated the correspondence

​🔷 identified the method used to express relations

​🔷 illustrated a relation and a function

​🔷 distinguished  functions from relations

​🔷 graphed and identified relations and functions

​🔷 identified functions based on their graphs

​🔷 determined the domain and range of a given function.​

Session Flow

Inspiring passage for the soul

​1. Quote of the Day

Advance Algebra Math 10A

​2. Exploration

Daily Waste Management Problem

​3. Structured Discussion

Input- Output

Relation Vs. Function​

​4. Drills

Journaling​

​(1) Quote of the Day

​(2) Exploration

How much waste would 8 adults generate?

Suppose 40 kg were generated in a day, how many adults were involved?

​(3) Guided Discussion

​How are the values of y related to the values of x?

What is the independent variable? Dependent variable?

​What equation represents the situation?

In the given situation, what is the input? output?

Questions!
Based on the video Input and Output

​Does each pair show relationship?

Questions!
Based on the video Input and Output

What relationships are being shown on the video?

Questions!
Based on the video Input and Output

What are the key terms you remember from each concept like, input, output, independent and dependent variable?

Questions!
Based on the video Input and Output

How is dependent variable and output the same? How about the independent variable and input?

Important Terms to Remember

​

▪ Input – values that we “put into” the equation ▪ Output – values that we “get/take/receive” from the equation ▪ Dependent Variables – variables that are affected by the other variables ▪ Independent Variables – variables that are not affected by the other variables

Function machines are used to apply operations in a given order to a value known as the input. The final value produced is known as the output.

Will you buy it?

​You were in a bookstore buying a very expensive pen. While on the line, The person in front of you is holding the same brand and style of pen you are buying. It was his turn paying for the pen he bought. Out of curiosity, to check the price of the pen upon scanning. It is worth Php 150.00. When it was your turn, you immediately prepared Php 150.00 from your wallet. To your surprise the item cost, Php 540.00

​What affects the difference in the prices of the two pens?

​Tip!

Subject | Subject

​Relationships are everywhere to be found. In our day to day living, we see and experience things or even people that are in relation to us. But are these relationships, functioning?

A Relation is a set of ordered pairs. Ordered pairs are usually written as (x,y).

Examples of Relations:

a. {(1,2) (2,4) (4,5) (5,3) (5,4)}

b. {(apple, red) (strawberry, red) (mango, green)}

c. {(Manila, Philippines), (Jakarta, Indonesia), (Bangkok, Thailand)}

A Domain is the list of all possible values of the x in a function. It is also referred to as the input of the relation or the independent variable.

Example: {(Manila, Philippines), (Jakarta, Indonesia), (Bangkok, Thailand)}

Domain is written in this form:

D: {Manila, Jakarta, Bangkok}

A Range is the list of all possible values of the y in a function. It is also referred to as the output of the relation or the dependent variable.

Example: {(Manila, Philippines), (Jakarta, Indonesia), (Bangkok, Thailand)}

Range is written in this form:

R: {Philippines, Indonesia, Thailand}

Fill in the Blank

What is the domain of the given relation?

{(1,3), (2,4), (3,5), (4,6)}

{

,

,

,

}

What is the domain of the given relation?
{(1,3), (2,4), (3,5), (4,6)} 

​Function

​is a relation in which each element of the domain corresponds to exactly one element of the range.

What is the range of the given relation?
{(1,3), (2,4), (3,5), (4,6)} 

Open Ended

Are all relation, function? why or why not?

​“ Every function is a relation but not every relation is a function.”

​Take Note!

Different ways in Identifying a Function

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​·  Ordered Pairs                            

● A graph                    

· A table of values                        

● Mapping Diagram

Ordered Pairs

​a composition of the x coordinate (abscissa) and the y coordinate (ordinate), having two values written in a fixed order within parentheses.

Multiple Select

Which of the following ordered pair represents a function?

• {(2,4), (2,6), (2,8), (2,10)}

• {(-1,1), (0,0), ( 1,1), (2,4)}

• {(-0.25, -1), (-0.3, -1), (0.5, 0), (1,1), (1.2, 1)}

Table of Values

​The rule to consider in determining whether a relation is a function or not in the table of values is the same as that of the ordered pairs and correspondence. There should be a unique output for every input. As mentioned, for the table of values, there should be two columns in which we put the values for the x and the values for the y.

Poll

Which of the following is a function?

• One to one

• One to many

• Many to one

​When dealing with functions, rules are present in a form of an equation. Sometimes, these are not explicitly stated in the problem or situation.

​Complete the table

​ y = x² + 1

​

Mapping Diagram

​Correspondence – this is also referred to as the pairing of the input and the output.

​Types of Correspondence

One to one – a unique value in the input is paired to a unique value in the output

One to many – a unique value in the input is paired to many values in the output

Many to one – many values in the input is paired to a unique value in the output

Many to Many – many values in the input is paired to many values in the output

Multiple Choice

Among the correspondence, which is not a representation of a function?

• one to one

• one to many

• many to one

Graph

​A function may also be expressed using a graph. If it is possible to draw a vertical line which intersects a graph in more than one point, we have the graph of a mere relation. If such a line cannot be drawn, we have the graph of a function

Vertical Line Test

​A graph represents a function if and only if no vertical line intersects the graph in more than one point.

​Which among the figures is not a function?

​Time to raise your concern

Multiple Choice

Determine whether each relation is a function.

• Function

• Not Function

Multiple Choice

Determine whether each relation is a function.

• Function

• Not Function

Multiple Choice

What type of correspondence can be illustrated in the relation

{(a, 1), (b, 2), (c, 3), (d, 3)}?

• many to many

• one to many

• one to one

• many to one

Multiple Choice

Which of the figure is not a function?

Fill in the Blank

Find the value of y in the function:

2x + 3y = 5 if x = 1

Open Ended

1.)    In my own understanding, the input is ________________ while the output is _______________________.

Open Ended

2.)    I am having a hard time with _____________________. I _________________ to overcome this difficulty.

Open Ended

3.)    Correspondence is important in relationships because  _____________

________________.

References

​https://slideplayer.com/slide/10502526/

https://ecdn.teacherspayteachers.com/thumbitem/Function-and-Not-a-Function-Graph-Math-Clipart-2683020-1568055243/original-2683020-2.jpg​

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