Graphing Funtion

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.

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, x².

The original function x² is in blue.

The vertical translation, function of y= x² +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= -x², shown in pink. I flipped the parent function graph across the x-axis.

The vertical reflection, function of y= -x² -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.

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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!

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. 

Ch.1 Real World Functions

For my Real World Function project I based my real world function on four National Football League teams and their corresponding hometowns.

A 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.

The x values or the football teams(Raiders, 49ers, Chargers, Seahawks) represent the domain/independent variable, while the y values or the home cities(Oakland, San Francisco, San Diego, Seattle) represent the range/dependent variable.

In a function there cannot be more than 1 element of y for every element of x. So, if Oakland and San Francisco were listed as the hometowns for The Oakland Raiders then the graph will not pass the vertical line test, therefore it will not be a function but, a relation.

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.

The Independent variables is the Monsters and the dependent variable is the health points.

The domain is the monsters snail, shroom, red snail, blue snail, green mushroom, and horny mushroom. The range is 15,20,25,50,80, and 200.

If the domain and range got switched it would not pass the vertical line test thus making it not a function.

Ch. P Graphing Functions by Ellie Cosine

For our chapter P project we had to graph using the parent 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.

The parent function that i will talk about is the Cubic function y=x^, represented in black.

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

About Me

The schools that i have attended were Lincoln Elementary school, Edna Brewer middle school, and now i attend Oakland High school. I do not have a job but i volunteer as a link crew member and what link crew does is help with school activities like registration or decorations. I would like to be a veterinarian or a nurse. I am not sure what yet but i am sure it will change in the future. Some interests i have are playing volleyball and badminton. These two are my favorite sports because i like how in volleyball you work as a team and it is pretty hardcore. I like to go out with my friends because they always make me happy. I love to read and my favorite books to read are the Harry Potter series and the Mortal Instruments series.

Chapter 1, Real World Functions

My real function is based on students and teachers in a 1st period classroom.

A 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.

The independent variable in my function are the students, the x value. While the dependent variable are the teachers, the y value.

The domain are the students- Lauren, Lucy, Nate, and Jack. The range are the teachers- Mr. Jones, Mr. Park, Ms. Taylor, and Ms. Lee.

The graph to the left is a function because it passes the vertical line test- the line only hits one point on the graph. The graph on the right is not a function, but a relation, because it doesn't pass the vertical line test and the line hits more than one point on the graph.

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 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.