Input and Output of a Function Graphically

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

Activity 2 & 3 (Worksheet)

Journaling​

​Tell Me Something That You Remember

​What are the things we learned on our previous meeting?

Advance Algebra Math 10A

​(1) Quote of the Day

Open Ended

Share your thoughts ...

​(2) Exploration

​Complete the table below

Draw

Complete the table

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?

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

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

Open Ended

Will you buy the pen? Why or why not?

​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?

Fill in the Blanks

What is the domain of the given relation?

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

Fill in the Blanks

What is the range 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.

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

Some text here about the topic of discussion

​·  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.

Poll

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.

Draw

Complete the table

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.

Draw

Draw a vertical line to each figure and identify if it is a function or not.

​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?

Draw

Find the value of y in the function:

2x + 3y = 5 if x = 1

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​

Some text here about the topic of discussion

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  _____________

________________.