2. WHAT YOU NEED TO KNOW
Determine functions and relations
Illustrate functions through mapping
diagrams, sets and graphs
Represent real-life situations using
functions
3. Across
2. the set of all x or input values
4. collection of well-defined and distinct
objects,
called elements that share a common
characteristic
5. The set of all y or output values
Down
1. is a rule that relates values from a set of
values (domain) to a second set of
values (range)
3. _______PAIR: pair of objects taken in a
specific order
WHAT’S IN
1.
2. 3
4.
5.
1.R
E
L
A
T
I
O
N
3 O
R
D
E
R
E
D
2. D O M A I N
4. S E T
5. R A N G E
14. SETS (Roster Notation)
f = {(0,-1), (2,-5), (4,-9), (6,-13)}
Function Not Function
R = {(a,0), (b,-1), (c,0), (d,-1)}
Function Not Function
NO x-value is repeated
15. SETS (Roster Notation)
g = {(5,-10), (25,-75), (50,-100)}
Function Not Function
It does not indicate a set. It is
simply a listing of ordered pairs.
16. SETS (Roster Notation)
T = {(-2,0), (-1,1), (0,1), (-2,2)}
Function Not Function
-2 (x-value) is REPEATED
17. SETS (Roster Notation)
T = {(3,3), (4,5), (5,5), (5,4)}
Function Not Function
5 (x-value) is REPEATED
28. FUNCTIONS IN REAL LIFE
Plants relay on the amount
of sunlight
“function of plants in sunlight”
29. Identify whether the relationship that exists
between each of the following pairs indicates
a function or not.
1. A jeepney and its plate number
2. A student and his ID number
3. A teacher and his cellular phone
4. A pen and the color of its ink.
30. What You Need To Remember
A relation is a function when every x-value is
associated to only one y-value
You can illustrate functions through graphing,
mapping or sets.
Functions can be seen in our daily lives like
driving a car, length of shadow and many
more
Editor's Notes
This presentation is for the first quarter lesson 1 of our subject General Mathematics the topic is Real life Functions.
What you need to know? We have 3 main objectives for this session the first one is youre going to determine functions and relations. Second Illustrate functions through mapping diagrams, sets and graphs and lastly is represent real-life situations using functions.
Whats in?
What you see in the screen right now is a crossword puzzle. So we have here five descriptions of different terms that is related to your junior high school mathematics these are necessary terms for us to proceed with our topic. Okay so you can answer this and try to recall those important terms i’ll give you 3 minutes. Are you done that sounds great so lets reveal the answers. So lets have number 1 down
Now to clarify about ordered pairs we have here an example remember that ordered pairs are a sequence of two elements like for this example 2 and 3 they are enclosed in a parenthesis and they are separated by a comma okay that’s an ordered pair. Lets proceed to the next one
When we say domain look at the example we have four sets or we have four ordered pairs in this set___ Now what is our domain here? Our domain are the first elements inside the parenthesis or first element in each of the ordered pairs so that means its 1, 2, 3, and 4 which serves as our domain.
We clarify about range now using the same examples for domain we have here this set of orderd pairs. Now this time the range is these values the second element of each ordered pair or the y values that will be 7, 6, 5 and 4 in this example
Whats new?
What makes relation a Function?
A function is a special kind of relation because it follows an extra rule just like a relation a function is also a set of ordered pairs however take note of this every x-value must be associated to only one y-value that’s the most important part of this lesson
Illustrations will help us a lot to learn functions easily so we have here mapping, sets and graphing. A function is special type of relation always remember that in which each element of the domain is paired with exactly one element in the range.
A mapping shows how the elements are paired its like a flow chart of a function showing the input and the output of values like this
The domain with the first set and the range for the second set now in this mapping lets identify if this is a function or not a function How do we do that? Lets recall the definition of functions every x-value must be associated to only one y-value so basing on that lets try to check if every elements in our domain is associated to only one value in our range. Lets focus on this part our domain -3 is associated to only one y value that is 0 so that is one is to one correspondence. So as you can see every elements in our domain is being paired to only one values of y in our range
Lets look at example number 2 can you identify if the given is a function or not a function?
This is still a function why looking at all elements of our domain -3 is being paired to 0, -1 is being paired to 4, 2 is being paired to 7 and lastly 4 is being paired to 4 so this shows that every element in our domain is being paired to only one value in our range. Which means if we have an input of -3 the output is only zero. If we have input -1 the output is only 4, if we have an input of 2 the output is only 7 and if our input is 4 our output is also 4. so this type of correspondence shows many is to one for this part we have two elements in our domain that has the same value in our range.
This is not a Function why earlier we saw many is to one correspondence right this time you call this type of correspondence as one to many it means 2 is being paired to -3 in the range at the same time the same element in the domain is being paired to 4 now that means this element in the domain has two outputs -3 and 4 which is not a function.
So this time lets move on to sets in this example we will have roaster notation.
So we have a set of four ordered pairs beginning with__Now can you identify if this given set is function or not function. Because these values in a domain should No x value is repeated.
So again the first step is lets identify the domain or the x values so meaning all the x values in our ordered pairs we have -2, -1, 0, and -2. now notice that here -2 is repeated that’s the x value its repeated for that element in our x or in our domain we do have two different outputs which is not anymore the definition of a function so this is not a function.
So again the first step is lets identify the domain or the x values so meaning all the x values in our ordered pairs we have 3, 4, 5, and 5. now notice that here 5 is repeated that’s the x value its repeated for that element in our x or in our domain we do have two different outputs which is not anymore the definition of a function so this is not a function. We are done with the second illustration for sets.
Again we are done in mapping and sets. Now this time lets focus into another way that’s for graphing. How do we identify if the given graph is a function or not your clue there is the VLT that would be our magic keyword to Identify if the graph is a function or not how what do you mean by VLT?
VLT stands for Vertical line Test. Functions can also be determined in graphing we can use this vertical line test which is a special kind of test using imaginary vertical lines and to check if these vertical lines would touch the graph only once otherwise it is not a function what do I mean by that if the vertical lines hits two or more points on the graph it is not considered a function. Lets look at some examples
So look at this graph. How would we know if this graph is a function or not Again what's our magic keyword? Well be using VLT that the vertical line test So that’s it the blue line that you see on the screen right now that’s an imaginary line, its not part of the graph we just made that line to test if the given graph is a function or not I hope you're following so the point there is here which means that the line the vertical line touches the graph at that point only once now lets move the blue vertical line because here you can check if it’s a function if any point of the graph it would only touch the graph or the given graph once. So lets move the vertical line. How about there yes it only hits once hence we can say that the given graph is a function so that’s an example of function basing on the graph.
Lets look at another example Identify if this graph is a function or not a function. Lets check lets create our imaginary vertical line again we will be using vertical line test right there the black dot represents the point where in the vertical line touches your given graph its only once right lets move it. It touches the graph only once basing on that we conclude that the given graph is function.
another example Identify if this graph is a function or not a function. Lets check lets create our imaginary vertical line again we will be using vertical line test right there the black dot represents the point where in the vertical line touches your given graph its only once right lets move it. It touches the graph only once basing on that we conclude that the given graph is function.
Lets use the vertical line test so lets observe this graph we have here two points which means that the vertical line test touches the graph or touches the given graph at two points if were going to move the vertical line test the vertical line is the same it touches the given graph at two points that means this is not function
Another example so to identify if it is function we use the VLT. So what do you is it function or not function? Okay so lets observe this graph we have here two points which means that the vertical line test touches the graph or touches the given graph at two points if were going to move the vertical line test the vertical line is the same it touches the given graph at two points that means this is not function
How about this graph is it a function or not function. It is not a function because the vertical line test touches the graph at two points.
How about functions in real life. The idea of a function can also be extended to real life situations. for example is a shadow the length of a person’s shadow along the floor is a function of their height.
Another example driving a car when driving a car your location is a function of time
The plants relay on the amount of sunlight so that means it is a function of plants in sunlight.
Function; A jeepney can only be assigned one plate number
Function; A student may only be issued one ID number
Not a function: A teacher may have two or more cellular phones
Not a function; There are some pens that have two or three colors of ink contained in only one unit.
