## Saturday, November 19, 2011

### Ch P Graphing Functions By Stephanie Ratio

The Ch. 0 Graphing Functions Project demonstrated how there are several different transformations for each of the five parent functions.

The original parent function is y = |x|, shown in the dark teal. The vertical translation, y = |x| -1, is the blue graph. y=|x| is shifted vertically down by 1 unit. The horizontal translation, y= |x-5|, is the purple graph. y=|x| is shifted horizontally to the left by 5 units. The vertical & horizontal translation, y = |x-2|+4, is the red graph. y=|x| is shifted vertically 2 units to the right and shifted horizontally 4 units up. The horizontal reflection, y = -|x| , is the green graph. y=|x| is flipped across the x-axis, making both the functions symmetric. The vertical & horizontal translation & reflection, y = -|x-6|-7, is the pink graph. y=| x | is reflected across x-axis, shifted horizontally to the right 6 units, and shifted vertically down 7 units. The vertical shrink, y = -2|x-3|+1, is the darker pink graph. There is a reflection over x-axis, a horizontal shift to the right 3 units, a vertical shift up 1 unit, and a vertical shrink by -2.

## Thursday, November 17, 2011

### About Me

Hi my name is Erika Huang.

Some previous schools I have attended are: Cleveland Elementary, Edna Brewer Middle School, and CSU Cal Maritime.

I am currently working at 4 different programs this year: PASS2 Mentors(where I work along with students at school to help peer mentor freshman, especially with graduation requirements), Da Town Researches (I go to many different public schools in Oakland and do a school quality review on specific schools then we try to help better those schools), AYPAL Campaign Organizing Team (I work along with 6 other interns where we deal with media stuff and campaign work. Our new campaign this year is Ethnic Studies), and Watershed Ambassadors (I teach little elementary school students about the then and now of Oakland).

When I go to college I want to major in Cell Biology and then after college, I'd like to be a pediatric nurse.

My main hobbies are just hanging out with my friends, traveling, and just relaxing. I really enjoy traveling because there are so many new things that I've never seen before and I'm always open to learning about different cultures!

### Chapter P Graphing Functions

During Chapter P, we reviewed some things that we learned from our previous math courses that would be applied in Math Analysis.

We had to do a project on graphing parent functions and performing translations on it. Some of the translations we did in this project was vertical shift, horizontal shift, and reflection across the x-axis.

My parent function was y=x^2.

- So the original equation is y=x^2 which is graphed in black.
- Then I performed a horizontal shift 7 units to the left so my equation was changed to y=(x+7)^2
- After the horizontal shift, I performed a vertical shift of 2 units up thus my equation came out to being y=x^2 + 2
- After my vertical shift up 2 units, I decided to shift it down 2 units from the original equation so it came out to be

y=x^2 -2 - After I did the horizontal and vertical translations, I decided to do a reflection across the x-axis so I multiplied the whole original equation by -1 so it came out to be y= -x^2

### CH 0 Graphing Functions, Yunny Power

This project was based on the parent** functions** in Chapter P. We had to make transformations from the parent functions. The **transformations** we had to create were **vertical translations, horizontal translations,** and **reflections **across the **x-axis** and** y-axis**. The parent function that I will explain about is the squaring function, x^{2}.

The original function x^{2 }is in blue.

The vertical translation, function of y= x^{2 }+2, is shown in orange. It was a vertical shift up 2 units.

The horizontal translation, function of y= (x-2)^{ 2}, is shown in magenta. It was a horizontal shift right 2 unit.

The vertical and horizontal translation, function of y= (x-2)^{ 2 }+1, shown in red. It was a horizontal shift right 2 unit, vertical shift up 1 unit.

The horizontal reflection, function of y= -x^{2}, shown in pink. I flipped the parent function graph across the x-axis.

The vertical reflection, function of y= -x^{2} -1, shown in green. It was a reflection and vertical shift down 1.

The vertical shrink and stretch, function of -2x(x+1)^{ 2 }-3, shown in purple. It was a reflection, horizontal shift left 1, and vertical shift down 5 and vertical stretch by 2.

'

## Wednesday, November 16, 2011

### Ch. 1 Real World Functions

My real world function is about time and destination.

A function is a relation where each value in the domain has exactly one value in the range.

A relation is a set of ordered pairs (x,y).

The independent variable(x) of my function is the time.

The dependent variable(y) is the destination.

The domain is [7:00, 7:15, 7:28, 7:45].

The range is [Burger King, Safeway, Lucky's, Applebee's].

The graph on the left is a function because it passed the vertical line test. All values of x has exactly one value of y. The graph on the right is a relation because it failed the vertical line test. The x-value cannot have two outputs of y.

### About Stephanie Ratio

Hi! My name is Stephanie Wong. The schools I previously attended were Cleveland Elementary and Edna Brewer Middle School. I am currently attending Oakland High School as a junior. I don't have a job but I have volunteered at the library and helped babysit my aunt's kids. Before, I wanted to become a nurse or a pediatrician since I like working with kids but now I am not sure. My favorite hobbies are spending time with family, hanging out with friends, and eating!

## Tuesday, November 15, 2011

### Real World Function

My real world function is the simple shape toys that children play with. For every specific hole on the box there is only one shape that would be able to fit through. This is an example a

**function**, a function is a relation that says that for every x value (domain) there is a specific y value (range). In this toy you can't put another shape into a hole that doesn't belong to that specific shape,for example you can't fit a triangle into a hole made specifically for a circle, this is a

**relation**, a relation is an ordered pair (x,y) that doesn't have anything specific.

## Monday, November 14, 2011

### Ch.1 Real World Functions

**function**is a relation for which every input there is

**exactly one**corresponding output. A function will also pass the vertical line test. A

**relation**is a set of ordered pairs.

**domain**/

**independent variable**, while the y values or the home cities(Oakland, San Francisco, San Diego, Seattle) represent the

**range**/

**dependent variable**.

### Chapter 1 Real World Functions

A function is a relation where each input have only one output . A relation is a set of order pairs.

### Ch. P Graphing Functions by Ellie Cosine

**functions**. We had to make different types of

**transformations**with the parent functions. The transformations we used were

**Horizontal and Vertical Translations**and we also

**reflected**them across the

**X-axis and Y-axis**.

First i translated the function 6 units down y=x^3-6, represented in light blue. Next i translated it to left 11 units y=(x+11)^3, represented in pink. Then i combined vertical and horizontal translations and shifted the function to the left 10 units and down 7 units y=(x+10)^3-y, represented in darker blue. Then i reflected the function across the x-axis y=-x^3, represented in green. Last but not least i combined vertical shift and reflection i moved the function down 9 units and reflected it across the x-axis y=-x^3-9, represented in purple.

### Ch. 1 Real World Function

My real world function is based on the the temperature of the room and the temperature reading displayed on the corresponding thermometer. The independent variable is the temperature of the room and the dependent variable temperature reading displayed on the thermometer .The domains for both graphs are 55 degrees Fahrenheit to 75 degrees Fahrenheit. The range for both graphs are also 55 degrees Fahrenheit to 75 degrees Fahrenheit. The graph on the left is a function (expresses the intuitive idea that one quantity [input] completely determines another quantity [output]) because each temperature of the thermometer reading accurately corresponds with one temperature of the room. The graph on the right is a relation (a set of ordered pairs) because the temperature on the thermometer does not match the temperature of the room, one temperature of the room had more than one reading on the thermometer, failing as a function and resulting as a relation.

### Ellie Cosine

### Chapter 1, Real World Functions

**function**is a relation of which each input of the domain corresponds with

**only one**output of the range. A

**relation**is a set of

**ordered pairs**.

**independent var**

**iable**in my function are the students, the x value. While the

**dependent variable**are the teachers, the y value.

**domain**are the students- Lauren, Lucy, Nate, and Jack. The

**range**are the teachers- Mr. Jones, Mr. Park, Ms. Taylor, and Ms. Lee.

**function**is a relation where an independent variable corresponds with

**exactly one**dependent variable and passes

**the**vertical line test.

A

**relation**is where an independent variable can correspond with

**more than one**dependent variable and

**does not pass the vertical line test.**

In my graph, Each burger at McDonald's has their own price, but some burgers are also priced as a dollar via the Dollar Menu we all know and love. So now there are 3 - 4 burgers that are entirely different but they all cost one dollar. The

**independent variables**, also called the

**domain**, are the price of burger. The

**dependent variables**, also called the

**range**, are the type of burger.

### Ch. 1 Real World Function

I did my real world function on a multicolored pen. The

**independent variables**are the variables that control the dependent variable. The independent variables, or

**domain**are purple, green, pink, orange, and blue which are the color of the switches. These are independent variables because they control what color of ink comes out of the pen. The colors of the switches are shown on the left side of the graphs. The

**dependent variables**are the range, which are purple, green, pink, orange, and blue. These are dependent variables because their outcome depend on the independent variable. We can see that the top graph is a

**function**because it always passes the vertical line test. Each domain has it's own value in the range. We can see that it's not a function because it does not pass the vertical line test, therefore it is a

**relation**.

### Ch.1 Real World Function

So I did my real world function on coins and the value of the coins. The

**Independent Variables**are the

**Domain**which is demonstrated by the name of the coin in this graph and the

**Dependent Variables**are the

**Range**which is the value in this case. The graph on the right is the Function graph and on the bottom it is a Relation graph. To tell the difference between 2 graph is rather if the graph passes the vertical line test which in this graph the dotted lines. Clearly we could see the bottom graph doesn't pass because the coins represented both value which could never happens. So when the graph doesn't pass it will be a Relation for Graphs that does pass it is a Function.

### Ch 1 Real World Functions

A function is a relation where an independent variable corresponds with exactly one dependent variable and passes the vertical line test.

A relation is where an independent variable can correspond with more than one dependent variable and does not pass the vertical line test.

In my function graph, each country has their own flag. However, Korea has two flags (one for each sovereign state N. Korea and S. Korea) as shown in my relation graph. The independent variables, also called the domains, are the countries. The dependent variables, also called the range, are the flags.

My real world function is on the color of passport and the meaning/status of the color. A function is a set of points in where every x-input have only one y-output. A relation is a set of ordered pairs.

The Independent Variable/Domain of my real world function is the color of the passport or the x-inputs.

The Dependent Variable/Range of my real world function is the status of color or the y-output.

The top graph represents a function in which every x-input have only one y-output and that it passes the vertical line test.

The bottom graph represents a relation in which every x-input have more than one y-input and it fails the vertical line test.

## Sunday, November 13, 2011

### Ch. P Graphing Functions By: Timmy Line

**Y=X^2**in red.

**The**

**second translation is**

**Vertical Translation**which moves vertically is in sky blue.Example Y=x^2-3. The third translation is

**Horizontal Translation**in pink

**which moves from left or right. Example Y=Ix-3I means it goes to the right 3 units. and vice versa for add. The next one is**

**Vertical Horizontal Translation**in green

**meaning it goes vertical and horizontal shifts. Example Y=Ix-1I+2I which is 1 unit to the right and 2 units up.**

**Horizontal Reflection**is -x^2 which is a relfection of the function in brown. The next one is a

**Vertical Reflection**which is in black Y=-Ix-2I. And lastly

**Vertical and Horizontal translation and vertical Reflection**which is Y=-Ix=1I-3 in black.

### About Yu Peng Circle

### Ch 1 Real World Function

**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.

### Ch 1 Real World Functions

A

**Function**is a set of ordered pairs where for every input (X), there are only one output (Y).

**Relation**is a set of ordered pairs.

**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).

### CH1 Real World Function

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.

### 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 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]

## Saturday, November 12, 2011

### Ch 1 Real World Functions

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

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

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

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

**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.

**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

Function: is a relation meaning each domain will have a range.

## Friday, October 28, 2011

### 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.

## Monday, October 24, 2011

### 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.

## Tuesday, October 18, 2011

### 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:

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.

## Monday, October 10, 2011

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.