Ch 0 Graphing Functions by Esther Infinity

In our Ch. 0 Graphing Functions Project, we illustrated the different transformation graphs of five different functions.
1. The original parent function is y = x².
2. The vertical translation, with a function of y = x² - 3, is shown in blue. I moved the parent function down 3 units.
3. The horizontal translation, with a function of y= (x - 3)² , is shown in red. I moved the parent function 3 units to the right.
4. The vertical + horizontal translation, with a function of y = (x - 3)² - 3, is shown in purple. I moved the parent function 3 units to the right and 3 units down.
5. The horizontal reflection, with a function of y = (-x)² , is shown in pink. I flipped the parent function graph across the x-axis.
6. The vertical reflection, with a function of y = -x² , is shown in green. I flipped the parent function graph across the y-axis. Also, since the parent function and the horizontal reflection would equal the same, they have the same graph.
7. The vertical + horizontal translation + vertical reflection, which a function of y = | x - 3 | - 3, is shown in orange. I flipped the vertical + horizontal translation function (purple) across the y-axis.

Ch. P Graphing Functions

This project shows graphs of different functions, with the functions we did different transformations.  
1.First I graphed the parent functions which was at the origin. y=x²
2. Then we graphed the vertical translation, which moved the parent function on the Y axis. y=x²+3 
3. horizontal translation is when the parent function is moved on the X axis. y=(x-3)²  
4. Both the vertical and horizontal translation are used.

5.  The Horizontal reflection reflects the Y axis. y=(-x)²   

6. Vertical reflection reflects the X axis. y=x² 

7. Vertical and horizontal translation and vertical reflection, this is graphed by applying the rules explain above. y=-(x-3)²+3   

About Jason Midpoint

I began school in Sebrante Park elementary but moved to several elementary schools which were garfield and franklin elementary. I also attended Roosevelt for my middle school years. I worked for Team Oakland during the summer and also volunteer at the Oakland Public library. When i grow up I want do create graphic art for videogames or maybe become a lawyer. My favorite thing to do is run and play basketball as well as playing videogames on my free time.

Ch. P Graphing Functions by Jason Helix

In our CH 0 project, we graphed parent functions. with the functions, we used the function to create a variety of transformations. The graph in top right corner shows the function in black, y=|x|. The blue is the vertical translation of the parent function, which is y=|x|+2. The red is the horizontal translation changing to y=|x-3|. The purple is both a vertical and horizontal translation making it y=|x-3|+2. The green one is a horizontal reflection, which goes across the y-axis, equaling to y=|-x|. The pink is a vertical reflection across the x-axis, forming y=-|x|. The orange one is a vertical and horizontal translation, with a vertical reflection, creating y=-|x-3|+2.

Ch. P Graphing Functions by Donald

In this project we had to draw transformations and each transformation contains a function. For example y= x^2 is the function for a parabola and y= |x| is the function for the V. I've drawn changes to the function and the orange parabola directly to the bottom of the center parabola is a vertical translation and and the green parabola directly to the left of the center parabola is a horizontal translation. There are four parabolas going up and two going down. The two going down are reflections of the parabola and both of which are in the negative x-axis. The y-axis cuts the 3 parabolas in the middle in half!

Ch. P Graphing Functions by Lan Expression

Our project for chapter P is graphing parent functions. In this project, we had to make some transformations to the parent functions. The transformations were Horizontal & Vertical Translations, and also Reflections across the X-axis and Y-axis. The parent function that I graphed was the Quadratic Function y= x^2 (Top left corner graph).

First, I graphed the original function (y=x^2) in black.

Then, I did a Horizontal Translation 4 units to the right in red which has the equation (y=(x-4)^2).

Next I did a Vertical Translation 5 units up in blue which has the equation (y=x^2 +5).

After that, I did a combination of both a Horizontal and Vertical Translation which makes the original graph shifts right by 4 units and up by 5 which is represented by the equation (y=(x-4)^2 + 5) in purple.

Now we go on with the reflections.

First, i did a Reflection across the Y-axis, it basically just flipped the original graph around across the Y-axis in green(on top of original graph in black) which look exactly like the original graph and gives us the equation (y=(-x)^2).

Then I did a Reflection across the X-axis which flips the original graph across the X-axis like the one in pink which is represented by the equation (y=-x^2). Last but not least.

I combined all the transformation made in this graph.

I did a Vertical and Horizontal Translation of 5 units up and 4 units right followed by a Reflection across the X-axis in orange which gives me the equation (y=-(x-4)^2 -5).

CH P Graphing Functions by Daniel

The function of this graph is Y=X^2 and our goal is to move it to different spot through translation and reflections which causes transformation in the graph.

1) The Vertical Translation is to move the Y=X^2 function vertically by adding a number. My graph shows Y=X^2+4

2) The Horizontal Translation is to move the Y=X^2 function horizontally by placing X in parentheses together with a number. My graph shows Y=(X-3)^2

3) The Vertical and Horizontal Translation is to move the Y=X^2 function both horizontally and vertically by putting step 1 and step 2 together which gives you Y=(X-3)^2+4

4) The Horizontal Reflection is formed when the function gets flipped around through the y-axis and gives us Y=(-X)^2

5) The Vertical Reflection is formed when the function gets flipped around through the x-axis and gives us Y=-X^2-2

6) The Vertical and Horizontal Translation plus Vertical Reflection is when Step 1,2 and 5 is added together and that gives us Y=-(X-6)^2-2

Ch P Graphing Functions

For our project, we had to graph the five parent functions, and this is one of them. Y= cube root of x. ( The last picture of the five)

1) This is the original function y= the cube root of x before any transformation, in the lime green color.

2) I then performed a vertical translation of 4 units up by adding it after the function, in purple color. See above.

3) Following after the vertical translation was a horizontal translation of 2 units left, shown above in the pink color.

4) The sky blue function shows the original function translated both vertically and horizontally.

5) The black function above is a vertical reflection of the original function.

6) The orange function is a horizontal reflection of the original function.

CH 0 Graphing Functions by Berenice Base

Our project was about the different types of parent functions.On these parent functions we had to preform transformations. The type of transformations that we had to do were vertical and horizontal translations.Also reflections over the x-axis and y- axis. One of these parent function that I graphed was the quadratic graph. It is on the far left. the original parent function was y=x squared.after graphing the original graph i did a vertical translation two units up. then i did a horizontal translation two units to the right.Then i combined the two to create a vertical and horizontal translation y= (x-2) squared + 2. After this i did a horizontal reflection y=-x squared. then a vertical reflection y=x squared. finally i graphed a vertical + horizontal translation + vertical reflection.

Ch. P Graphing Functions

Our chapter P project was to graph parent Functions. We had to we did our project on graphing parent do many different types of Transformations. My parent function was y = |x| which looks like a V shape. What I did first was to graph the parent function y =|x| which is in the middle covered by the brown line and the brown color is a Reflection across the Y-Axis or a horizontal reflection y=|-x|. Since reflecting across the Y-Axis for this function, it'll look exactly the same since it is symmetrical on both sides. My next translation was a Vertical Translation y=|x| + 3 where I move the function up by 3 indicated by the orange line. This shows that the function moved up by 3. Then I used the Horizontal translation y=|x-1| indicated by the red lines which shows the graph moved to the right by one. After that, I combined the vertical and horizontally translation together y=|x-1|+3 to move it up 3 and right one shown by the green line. After doing that, I made a reflection across the X-Axis y=-|x| which flips the equation upside down shown in blue. The last transformation what a vertical, horizontal translation, as well as a vertical reflection y=-|x-1|+3 where I move to the right one, up 3, and flip it outside down

CH P Graphing Function

In class, we were graphing functions of different kinds of transformations.

The picture shown to the left is the function y=x2 (squared).

1.)The original function is y=x2 which is in black.

2.)Then, up next is the transformation to vertical translation which is shifting up or down the units given. My equation is y=x2 + 3 which is shifting the y-axis up 3.

3.)The next transformation is the horizontal translation which is taking the given function and shifting it left or right by units given. My equation is y=(x-7)2 which shifted 7 units right in the x-axis. When X is subtracting a number given, then it is going to the right, but when it is adding a given number, then it goes to the left.

4.)I then combined an equation with vertical and horizontal translation. My equation i chosed was y=(x+3)2 - 2. This equation is shifted 3 unites to the left and 2 units down. To do this equation is the same as the ones above, but instead, I put both transformation together in one equation.

5.)The graph that looks upside down is the reflections. reflection is given when the given function is negative. My equation shows y= -x2. This equation is just the opposite of the original equation. They are ''reflecting", folding your paper hamburger style shows the reflection vertically.

6.) There is also an horizontal reflection, which is the having an negative X in an equation. For example, look at my original function, there is also another color outlining it which is y=(-x)2. This is the reflection horizontally, it is like folding your paper hot dog style, getting a mirror image.

7.)The last graph showed is combining both translations and reflections together. My equation shows y= -(x-4)2 - 2. This is pretty much the same as combining both the horizontal and vertical translation but yo also include the reflections together.

In conclusion, this shows the different transformation for the parent function y=x2(squared).

Ch. P Graphing Functions by Thanh Quotient

For chapter P, we did our project on graphing parent Functions. We had to perform Transformations: both Vertical and Horizontal Translations, and Reflections across the X-axis and the Y-axis. One of the parent functions i graphed was the absolute value parent function (the picture on bottom left of the first picture). The original parent function was
Y= |x|. I first did a vertical translation by moving the graph up by one unit and adding 1 to the function outside of the absolute value sign:
Y= |x| + 1, next i did a horizontal translation by moving the graph one unit to the right and subtracting a 1 from the x inside of the absolute value sign: Y= |x - 1|, I then combined these two vertical and horizontal translations and moved the graph up one unit and one unit to the right giving the equation Y= |x - 1| +1. Then i did a reflection across the Y-axis (also known as a horizontal reflection) which did not change anything except for the equation of the parent function which turned the "X" inside of the absolute value to negative giving us Y= |-x| and i also did a reflection across the X-axis (also known as a vertical reflection) which flipped the graph upside down below the x-axis, this changed the absolute value parent function into Y= -|x|, where the negative is outside the parent function. Finally i did a vertical and horizontal translation with a vertical reflection where i moved the original parent function one unit up and to the right flipped upside down below the x-axis before i perform the translations, giving me Y= -|x - 1| - 1.

CH 0 Graphing Function

What we are trying to do here is to show the different transformations of a function
The function that I use is y=| x |, this function is to show how the graph will look like when x is an absolute value and it will show what kind of answer will you get when you plug in x.

1. The original function is in Yellow, showing you were did I began at.

2. Then we transform the original function into a Vertical Translation, which is stated in penish color and the equation is y=abs(x)+1. ( y=| x |+1 ). In a vertical translation you could determined how many space to move on the Y-axis by positive or negative integers.

3.From Vertical Translation we went back to the original function graph and move to the right and formed Horizontal Translation and the equation is y=abs(x-2). ( y=| x -2| ). You could see that in pink. For horizontal translation you could determine whether you should move right or left is by looking at what "x" is doing. If "x" is subtracting then you will move to the right on the x-axis, and left if you are adding.

4.The next one is going to be hard to see because it is in orange and that one is the Combing Vertical and Horizontal Translation. The function is y=abs(x-5)+2. ( y=| x- 5 |+2 ). From the explanation above of Vertical Translation and the Horizontal Translation, all you need to do is to combing the directions and you will have your combination of the vertical and horizontal translation.

5. This one is a Reflection over the x-axis the color is in light blue the equation for this one is y=-[abs(x)]. ( y= -| x | ). Basically you are just opposing the original function.

6. There are also a Horizontal Reflection, the color is yellow and you can use barely see it but it is there. The equation for this one is y = abs(x). ( y= | x |). So now you could understand why is the line is kind of limeish color because it is a mixture of green and yellow and it is basically the same line.

7. The last one is a Combing Translations and Reflection. It is in the color of dark green, the equation for this one is y= -abs(x-5)+2. ( y= -| x - 5|+ 2). It is similar to the horizontal and vertical translation except you are putting them in a opposing side of the original.

From all of that is the explanation of the color and what I did, I didn't explain about the red one, because that is just a reflection of the vertical translation.

CH P Graphing Functions

1) The original square root function before the transformations is in brown color.

2) I perform vertical translation up 4 units, by adding 4 outside of the square root. See the function in blue.

3) I translated the square root of x horizontally 3 units to the right by subtracting x by 3

inside the square root symbol. See the function in red.

4) The purple function show the vertical and horizontal translation of the square root function together. I subtract 3 to x inside the square root and added 4 outside the square root symbol to do so.

5) The graph in green is the horizontal reflection. This reflection across the y- axis could be created by putting a negative sign in front of x, like this (-x).
6) The vertical reflection across the x-axis is in pink. To get this function we have to multiply the square root of x by -1.

7) The orange function is 4 plus the negative square root of x minus 3. In other word this is the vertical reflection and horizontal/vertical translations of the square root function.

Graphing Functions

1) The black graph is the function of y=x².

2)The orange graph is the function of y=x²+4. This is both a Transformation and a Vertical Translation of the function y=x². To perform this translation, add a number(in this case, 4) to the function. This will be the y-intercept.

3)The red graph is the function of y=(x-3)². This is both a transformation and a Horizontal translation of the function y=x². To perform this translation, place X in parentheses and add a negative number to translate it left or a positive number to translate it right(in this case, -3), then square the parentheses.

4)The green graph is the function of y=(x-3)²+4. This is a transformation, vertical, and horizontal translation of the function y=x². To perform this, combine both a vertical translation and a vertical translation by doing the processes of each on the same graph(in this case, putting X in (x-3) and squaring it for the horizontal translation and adding 4 for the vertical translation).

5)The brown graph is the function of y=(-x)². This is both a transformation and a horizontal Reflection of y=x² which reflects over the Y-Axis . To perform this, multiply x² with -1 and place it in parentheses and squaring it. Since y=x² is horizontally symmetrical, there is no change in the function when horizontally reflected.

6)The blue graph is the function of y= -x². This is both a transformation and a vertical reflection of y=x² which reflects over the X-Axis. To perform this, multiply x² with -1.

7)The purple graph is the function of y=-(x-3)²+4. This is a transformation, vertical translation, horizontal translation, and vertical reflection of the function y=x². To perform this, multiple steps are required. First, add 4 to X to make a vertical translation. Next, for the horizontal translation, place X in parentheses and add -3. Finally, for the vertical reflection, multiply the parentheses containing X with -1 and square it.

0 How to Do Graphing Functions

Choose one of the five functions you graphed on the Graphing Functions Project.

1. Describe what you did using mathematical vocabulary. The following words must be used correctly, and highlighted or boldfaced in your description.

function
transformation
translation
vertical
horizontal
reflection
x-axis
y-axis

2. Include  all 5 pictures of your scanned graphed functions in your blog.

3. Back to School Night Extra Credit - Scan your Parent's classwork into your blog. Write a few sentences about what you and your parents thought about learning transformations.

4. Choose CH 0 Graphing Functions and your Name to label your post.

Timmy Line

My name is Timmy Line. The first school I attended was Bella Vista elementary school. Then I went to Edna Brewer middle school. Now I’m attending Oakland high school. I am currently working for EBAYC after school program at Garfield elementary school. I help kids on their homework and teach enrichment. I get paid at $8.25 an hour. I also had done some volunteer work with ESA. When I grow up I want to major in business and marketing and run a business. I really enjoy playing sports when I have time. I really enjoy playing basketball the most because there is a lot of running involve. I also enjoy playing baseball, football, tennis and sometimes volleyball if I and my friends have time to play. A hobby I like is collecting shoes. Which I really enjoy doing.

TAM EQUATION

Hi!!! My name is Tam Equation. I have attended Quang Trung Elementary School in Vietnam, Roosevelt Middle School, and now i'm a 11th grader at Oakland High School. I've never had a job or volunteer. I want to be a fashion designer,  but somtimes i want to be a nurse. I am still confused between both of these. My favorite thing to do is sleep, I can sleep all day.  Also, I like to sing, and play games online. 

About Ivan Radius

As a child, I went to Cleveland Elementary school. Later, I went to Edna Brewer Middle School. Once I've graduated from there, I went to Oakland High School and am currently a junior in the class of '13. I've never volunteered or had any jobs. When I grow up, I want to be a lawyer. My favorite things to do are hang out with friends or play video games.

About Clinton Medium

I attended Lincoln Elementary, Edna Brewer Middle School and is attending Oakland High as a junior, class of 2013. I do not have any job experiences but I have volunteered in a day care and the Oakland Library. I am unsure of what I want to be when I grow up. I enjoy going on the computer, playing video games and hanging out with friends playin a game of 13.

Jason Helix

Hi, my name is Jason Helix. I have attended Garfield Elementary School, Roosevelt Middle School, and am currently enrolled in Oakland High School as a Junior of the class of 2013. I haven't had much work experience or volunteer jobs, except for the occasional E.S.A. related volunteer jobs. My future is still a mystery to me and have no immediate job or occupation that I want to be involved with, but at some point of my childhood, I wanted to become a pilot and take control of my very own aircraft. One of my favorite things to do is to swim. Even though I complain about how difficult it is, I still enjoy the feeling of being weightless, and drift off into the deep blue.

Courtney Log

My name is Courtney Log. The elementary school i attended was Glenview, then went to Edna Brewer for middle school, promoted, and is now an 11th grader in Oakland High School (Woot! class of '13). I can't recall anything I have volunteered at, however I know I have done some in ESA (ie. Earth Team). I still don't know what career to pursue, but I'm leaning towards the medical field or an office job. In my free time I like to go on the computer, play video games, or read a good book. (But who has free time these days?)  

About Kevin Torque

Hey, my name is Kevin Torque. I started off as a student in Manzanita Elementary, got a little older and began attending Edna Brewer, until I found myself here at Oakland High School. I am a Junior in the awesome class of 2013! I have volunteered a lot of my time with the American Red Cross and College Track, and I have also gotten my first job as a youth media intern for the Museum of African Diaspora in San Francisco. Since I was young I've always wanted to be a physician; just reading through my mother's biology and human anatomy books as a child always had me interested in the human body and how it functions. Like any guy in this century, I like to play video games with friends, but I also enjoy taking leadership positions. I've taken leadership positions since I was in the 6th grade, and I've always loved the adrenaline and sense of accomplishment that comes with being a leader in general.

About Kevin Fraction

Hi, my name is Kevin Fraction. As a student, I have attended Bella Vista Elementary, Edna Brewer Middle School, and now I am currently attending Oakland High School. I am a Junior and will be graduating in 2013. I remember volunteering in creek restoration as an ESA student, but other than that, I haven't actually held any jobs nor have I volunteered much. But I am looking forward to achieving some community service hours this year! As of now, I have my future career set on Law Enforcement. I want to serve my community as a police officer - ensuring people's safety and health, enforcing laws, and all that good stuff. One of my hobbies is sports. I prefer contact sports, so football, wrestling, or boxing is what I like the best. But I can have fun with any sport. I really like participating in physical activity. There's nothing wrong with getting a nice workout, right? I like to be outside where I can enjoy nature. I like hanging out with family or friends. And if I'm not doing any of those, you can catch me at home sitting in front of a computer playing games.

Daniel Triangle

My name is Daniel. Previous schools that I have attended is Cleveland Elementary and Edna Brewer Middle school. I have never worked in a paid job before but i have volunteered to work in my cousin's house to clean his room. I am not 100% sure what I want to be when I grow up but I might become an engineer. I have many different hobbies including badminton and outdoor sports. Some indoor hobbies would be playing computer games like League of Legends, OMGPOP, etc. I also like to troll people online.

About me, Donald Polygon

My name is Donald Sun. I attended Lincoln Elementary and Edna Brewer middle school. I attended Aypal the whole year, which gave me about 80 hours of community service. Aypal is basically a program that fights social injustice like all the -isms, Racism, Heterosexism. When I grow up, I actually want to attend UCLA hoping to major in business and financing. But since the economy in the U.S is so bad, i've been rethinking about this. If I do get into UCLA, i want to eventually be a C.E.O for a major company, or the job below the C.E.O so I dont have that much things to deal with! My hobbies is learning how to strengthen my leadership skills, having the skills to be confident. Getting to know people and making new friends.