About Yu Peng Circle

Hi.My name is Yu Peng.I went to Bella Vista as my elementary school and Enda Brewer as middle school. I don't had any jobs but I would like to get one.When I grow I want to be a doctor or a teacher.My hobbies are badminton,read books,and play computer game.

Ch 1 Real World Function

This is my real world function project about the different types of sodas under Pepsi Co and the amount of calories they each have. A function is the relation between x and y, where for every input value of x, there's only one output value of y. A relation is a set of ordered pairs. The independent variable in this project is the different sodas, also the x value. The dependent variable is the amount of calories it has, the y value.

The upper graph shows that when each soda only have one value of variables, it is a function, but the lower right graph shows that there could be two input, in this case, two different soda with the same name, for example, mountain dew and diet mountain dew, and they both have different calories, which makes it not a function. You can see that the upper graph passes the vertical line test but not the lower right graph.

This function has a domain which is (Mountain Dew, Citrus Blast, Pepsi, Brisk, and Sierra Mist). The range is (110, 140, 100, 80, 100) in it's chronological order based on it's domain because each soda has a specific value of calories.

Ch 1 Real World Functions

My real world function is about high school and their school mascots.
A Function is a set of ordered pairs where for every input (X), there are only one output (Y).

A Relation is a set of ordered pairs.

The Independent Variables are the Domain of the Relation/Function which are represented by the X-Values (Input).
The Dependent Variables are the Range of the Relation/Function which are represented by the Y-Values (Output).

The left table and graph represents the Function of this project. the Indepdendent Variables are the Mascots and the Depdendent Variables are the high schools that uses the mascot.

The right table and graph represents the Relation of the project. The Relation represents why the Function would fail. This Function failed when the same mascot is being used by 2 schools.

The dotted line of both graphs represents the Vertical line test which helps us determine if a graph is a Function.

As you can see. the graph on the left passes the vertical line test but the graph on the right doesn't because there are 2 points that touches the vertical line which tells us that it is not a Function.

CH1 Real World Function

In this Project, we had to find an example of a real world function, and I chose the page number of a book called Pre-Calculus: Graphical, Numerical, Algebraic by Demana, Warts, Foley, and Kennedy.

Every time we turn the page in the book, we land on a certain section of a certain chapter, and in this case, I chose chapter 1.

For my example of a function (on the left) there are a certain amount of page numbers to be turned to end up on a certain section, but every time i flip a certain amount of pages to get to a chapter, I always started in the beginning page. A Function is a set of all points (x,F(x)) where each input as "x" has exactly one output which is represented as Y or F(x).

For my example of a Relation (on the right) which is a set of ordered pairs, which is not a Function, I used the same book to flip 70 pages to get to chapter 1.1, ;however, when I flipped 70 pages again, I did not land on chapter 1.1, i ended up on chapter 1.5, and when I flipped 70 pages again, I was found on a whole new chapter. This shows that it is not a relation because for every 70 pages i turn, i get more than one output, which goes against the rule of a function having one output for every input, in addition, it also fails the vertical line test, therefore, it is a relation.

The Independent variable in these two graphs are the page numbers, and the dependent variable were the sections of the chapter.

When i graphed out all of the coordinates, for my function example, i got a line that passes the vertical line test, meaning, it is a function. I got the Domain: [0,163] and the Range: Chapters: (1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7) U (2.3), but the relevant Domain to the function on the left was [70,163], and the relevant Domain for the relation on the right was only 70. This shows a basic idea of the difference between a Function and a Relation.

Ch1 Real World Functions

In this function, countries and their populations in 2010 are being compared.
A function is when the values of the domain produce only 1 range value.
A relation is a set of ordered pairs.
In the function, each country only has 1 population.
It fails as a function when the countries have more than 1 population, which is impossible. It becomes a relation.
The independent variables are the countries.
The dependent variables are their populations.
The domain is {China, India, US, UK, Russia, Mexico}
The range is [100k, 1.3m] because the lowest population in the 6 countries chosen is 100k(U.K) and the highest is 1.3m(China).

Ch 1 Real World Function

The graph on the top is a function where it shows the place of the work and how much the person gets paid and that for every x-value there is exactly one y-value.

The graph on the bottom is also about the pay and work but it is a relation since it showed for some x-values, there are two to three y-values on a point.

A relation is a set of ordered pairs (x,y).
A function is a relation for which each element of the domain (x) corresponds to exactly one element of the range (y).
The independent variable is the places of work.
The dependent variable is the amount of pay for work.
Domain - [Happy Teeth, Youthful Teeth, Western Dental, Central View]
Range - [12.67-20.78]

REAL WORLD FUNCTION 

Function- A relation that associated each value in the domain with exactly one      

             value in the range.

Relation- A set of ordered pairs of real numbers.

     

Ch 1 Real World Functions

My real world function is about the type of hair clip/comb used on a person's head.

The domain for this function is (0, 1, 2) which is the type of hair clippers.

The range is (0,1,2) which is the setting of the type of hair clipper used on a person's head.

The independent variable in the graphs is the type of hair clip/comb used.

The dependent variable in the graphs is the type of hair clip/comb used that appears on a person's head.

The definition for a function is a relation for which each element of the domain corresponds to exactly one element of the range.

• The graph on the left is a function because for every x-value, only 1 y-value responds and it passes the vertical line test.

The definition for a relation is a set of ordered pairs.

• The graph on the right is a relation. This graph is only a relation and not a function because the x-value hits the graph at 2 point which shows that it didn't pass the vertical line test.

Ch 1 Real World Function

For my real world function I decided to do mines on one phone number goes to one person. The domain for this function is ( 511,777-3333,596-3700) . The range is the (Info. place, Oakland police department, Emerville police department). Definition for function is a relation that associates each value in the domain with exactly one value in the range. The first graph to the left is a function because there is exactly one domain for each one range. Not a function would be that if your phone is acting up and when you call one person your phone is calling three people at the same time when you only dialed one number. As you can see there is a second graph and the second graph isn't a function because there is only one domain for all the ranges. Definition of a relation is a set of ordered pairs of real numbers. The independent variable in this function is the phone number that you are dialing. The dependent variable is the person who picks up.

Ch 1 Real World Functions

Definitions:

Relation: a set of ordered pairs
Function: is a relation meaning each domain will have a range.

The graph on the left shows the domain of language classes and the range as the language spoken in class. The independent variable will be the language class and the dependent variable will be the language. This graph shows that each domain (spanish class, cantonese class, french class, and german class) will have one range ( spanish, cantonese, french and german).

The graph on the right shows the same thing as the left but there is one domain that have two ranges. Which is called a relation. Cantonese class have Cantonese and French being spoken.

About Yunny Power

Hello! My name’s Yunny Power. I’m currently a Junior at Oakland High School. The schools I attended were Bella Vista Elementary and Edna Brewer Middle School. I have attended many community services, and tutored my neighbor's kids. I'm not getting paid, but the feeling of being able to help those in need feels wonderful. I'm in Oakland High's KIWIN'S, and been a member of AYPAL for two years. When I get into college, I want to major in the Marketing or Psychology field. My hobbies are the typical things everyone else loves to do- spending time with their friends and family.

Ch 1 Real World Function

Definitions:
Relation is a set of ordered pairs.
Function is a relation for wich each element of the domain corresponds to exactly one element of the range.
The graph on the right shows the 6 flower species as the independent variables and their native habitats as the dependent variables. The domains are the flowers: plum blossom, lotus, musk rose, ixora, prim rose, foxglove; the ranges of the function are the countries: China, India, Malaysia, England. Since each of these flowers had 1 original nativity this is a function.
In the graph on the right I added the bombax ceiba flower specie, which was distributed in 3 places. The domains are now including plum blossom, lotus, musk rose, ixora, prim rose, foxglove, and bombax ceiba; the new ranges are China, India, Malaysia, England, and Australia. Since 1 of the domain had match with more than 1 range, the function failed and the graph is a relation.

1 How to Do Real World Functions

1. Choose a real world function
2. Describe and draw a picture for your function.
3. Describe and draw a picture when your function fails (i.e. when it is a relation not a function)
4. Include the definition of function and relation in your descriptions for 2 and 3
5. Identify the following:

Independent Variable

Dependent Variable

Domain

Range

6. Draw a graph of your function on the Cartesian Coordinate Plane

Note: see An Example Student for an example of how to do this project.

Ch0 Graphing Functions by Tam Equation


For the Ch.0 Graphing Functions. I'll show the 


different transformation of a function.


_The original Function is y = x^3 


_The Vertical Translation, the function is 


y = x^3 +2. I moved it up 2 units.


_The Horizontal Translation, the function is 


y = (x+2)^3. I moved it 2 units to the left.


_The Reflection, the function is -x^3. I just flipped


the original across the y-axis. 

_The Vertical + Horizontal, the function is 


y = (x+2)^3 -3. I moved it 3 units to the left and 


down 3 units. 

_The Translation + Reflection, the function is

y = -(x+2)^3 +3. I moved it 2 units to the left and 


up 3 units.

Chapter O Graphing Functions by Clinton Medium

In Chapter 0 we learned about transforming parent functions. The original equation was y=|x|. The vertical translation of y=|x|+2 is moved up by 2. The horizontal translation of y=|x-2| is moved to the right by 2. The reflection of y=-|x| is reflected across the x axis. The combination of Vertical land Horizontal of y=|x+3|+1 is moved up by 1 and to the left by 3. The vertical stretch of y=|2x| is stretched by 2.