Lord of the Flies

Posted on by shannonf2015

Three Reasons Why I Would Want Ralph as my Friend

 

If I was stuck on an island with a group of boys (what a nightmare!), I would want Ralph as our leader. Why? Because he’s intelligent, understanding and organized. He doesn’t let the influences of the other boys affect him,  only until the end with the feast, but what can you do? No one is perfect and at least he recognised what he had done unlike the rest of the boys. He guides the group with his top priorities and treats everyone equally. What better leader could you ask for?

 

1. He has Common Sense and is Quite Mature
 Image result for thinking about survival cartoon

http://www.roguesurvivor.com/wp-content/uploads/2015/08/survival-situation-use-your-head.png

Ralph is quite a mature kid for his age. Instead of playing around and having fun on the island like probably any  other boy would, Ralph focuses on survival. Even though he’s like thirteen, he acts like an adult. He holds meetings where he proposes the signal fire in order to get ships’ attention and is the first to realize they need a leader on the island. Who would’ve thought of making a signal fire? Any other boy would’ve probably started playing tag or cry due to loneliness. He’s like the older brother of the group, not as strong as Jack but at least he uses his head and not intimidation. He continues to tell the boys they have to keep the signal fire going which becomes a new goal for the boys and he uses the idea suggested by Piggy about building huts for shelter. Ralph also speaks up when needed to like when he approached Jack because he was only focusing on hunting and didn’t keep the fire lit. His maturity is shown through how he takes action by confronting Jack and his tribe. Overall, his intelligence and maturity makes him a very trustworthy leader who knows what’s best for the group. Way to go Jack! I’m definitely sticking with this guy.

 

2. He is Organized

Image result for checklist cartoon

https://i2.wp.com/www.humanengineers.com/wp-content/uploads/2015/12/checklist-cartoon.gif?fit=288%2C276

Ralph is so organized I just don’t understand. Although not everyone listens to him, Ralph makes an effort of setting rules and boundaries in hopes of keeping everything in order and at peace. He is so organized it’s unbelievable, I would definitely like to be his friend. He stays on topic and doesn’t easily get caught up with theories or questions like how Piggy does. Thank goodness! He has priorities which allows him to lead the group with success. Even when the beast was introduced, he didn’t let it affect him. That’s some incredible self-control right there! He guides the group of boys and keeps them in line by focusing on survival. He makes the rule that only the person with the conch can speak and may not be interrupted. (Again, he is so mature!) His true leadership is demonstrated by his awareness that there must be restrictions and laws in order to maintain a civilized society to avoid chaos. He also gives out specific tasks such as making sure that they are keeping the fire burning and even makes specific areas a place to go to the bathroom, to keep potable water as well as building the huts in order to keep the island organized and tidy. He treats the island like a new home while giving everyone chores including himself. Such an organized thirteen year old!

 

3. He Treats Everyone with Respect

Image result for listening to others cartoon

http://skillgames.playgen.com/wp-content/uploads/2016/04/introducting-others.jpg

What makes him such an awesome leader and friend is his leadership style. He gives everyone a chance to share their opinions and to be part of making decisions. That’s the definition of a true leader and friend. He treats everyone equally and defends those who are too weak like when Jack was bullying Piggy (Poor Piggy!). Even though Ralph didn’t like Piggy in the beginning, he starts to value his opinion and him as a friend. He is able to consider each opinion before making decisions. For instance, when Ralph was voted chief, he could tell that Jack had the desire to have control over something by the way he was blushing, so he let Jack lead his choir of hunters. It’s amazing how Ralph can be so thoughtful with such an intimidating, arrogant and mean bully like Jack. He is open minded even with the opposing political party and doesn’t make decisions until everyone contributes their opinion. I would’ve probably started ripping my head if I had to deal with a meanie like Jack, that’s why I need Ralph to help me calm down. This goes to show that Ralph is an easy going guy who is willing to listen to anyone. Wouldn’t everyone like to be treated equally like how Ralph treats his group? I know I would.

Week 18 – Precalculus 11

Posted on by shannonf2015

Top 5 things I have learned in Precalc 11

  1. Graphing: Is the number one thing that I learned. This semester, I found graphing straightforward and eyeopening.  I learned that once you find the vertex, you just have to follow the 1,3,5.. pattern and multiply the pattern if it has a stretch or compressed value (number in front of the x^2). I learned that you could find the number of solutions which is also the x-intercepts, as well as the vertex which is a key component to graphing. This made graphing absolute values easy as well as reciprocal graphs. It was really cool to see I could graph all these different types of graphs with just some information given.

2.  Substitution: Solving systems with substitution was another thing I learned in precalc instead of drawing the graphs out. I finally knew how to solve systems algebraically which made me feel more knowledgeable about solving systems and it became a useful tool if I didn’t have graph paper to graph out the systems.

 

3. Completing the squares: I never realized how important completing the squares was. We used it a lot during this course such as changing general form into standard form to get the vertex, to find the axis of symmetry, and to solve an equation. It does take awhile when it comes to solving an equation, however, it still is a useful tool when it’s an equation is unfactorable and I found myself using it a lot when I had to find the vertex.

4. Trigonometry: The most important lessons I got out of this chapter is the Sine Law and Cosine Law. They were very useful when it came to scalene triangles and I found solving sides and angles a lot easier than I thought it would. I am now able to tell when to use Cosine Law and Sine Law (Cosine – when three sides are given or two sides and a contained angle are known; Sine – when two angles and one side are known or two sides and a non-contained angle are known).

5.  Square roots : Whenever we were solving an equation and we had to square root both sides to get the variable by itself, there was both a positive and negative sign in front. Before, I always treated a square root as having one answer but now I realized that there are both positive and negative values (only when I add in a square root but if there is already a square root, you take the positive roof of it). Even though it is a simple concept, this was a big eye opener for me.

Week 17- Trigonometry

Posted on by shannonf2015

This week we have learned the primary trig ratios (Sine, Cosine and Tangent), how to sketch angles in standard position, as well as sine law and cosine law.

Let’s look at the primary trig ratios:

Before we used SOH CAH TOA to remember the ratios for trig, now we have replaced the opposite angle with y, adjacent with x and the hypotenuse is replaced with r.

Sineθ: \frac{y}{r}

Cosθ: \frac{x}{r}

Tanθ: \frac{y}{x}

We have also learned CAST which helps with determining if the angle is positive or negative, the two triangles used to determine the trig ratios and a diagram that can be used to determine the primary trig ratio when an angle has its terminal point on the x-axis or the y-axis

 

Example when using the two triangles:

\tan{150^{\circ}}

We must first find the reference angle and determine which quadrant the angle is in. It is in quadrant 2 so we must take 180 and subtract 150 degrees which gives us 30 as the reference angle.

If we look back at the two triangles, we can see that the triangle that has 30-60-90 will be the triangle we must use. Looking at the 30 degree point of the triangle, we can start labelling the sides of the triangle to find the ratio.

 

Remember that tan’s ratio is \frac{y}{x}. y will be 1 and x will be \sqrt{3} . When we look at CAST, we can tell it’s going to be negative because 150 is in the second quadrant (only sin is positive in second quadrant). So the ratio will be \frac{-1}{\sqrt{3}}.

 

Let’s look at another example using the unit circle for quadrantal angles.

\cos{130^{\circ}}

The ratio for cosine is \frac{x}{r}. Look at where angle 180 is which has the point (-1,0), where x=-1 and y=0. r is always going to be positive for quadrantal angles. So the ratio is going to be : \frac{-1}{1} = -1.

We have also learned how to find the reference angle of each quadrant. Let’s look at an example:

If the reference angle is \cos{43^{\circ}}

Quadrant 1: It’s going to be the reference angle : \cos{43^{\circ}}

Quadrant 2: 180 – 43 = 137

Quadrant 3: 180 + 43 = 223

Quadrant 4: 360 – 43 = 317

To know when to use Sine Law, we have to be given at least one angle and side that is across from each other. For Cosine Law, we need either three sides or at least two sides and an angle.

Sine law: \frac{SinA}{a}=\frac{SinB}{b}=\frac{SinC}{c}

We have the degree on the top if we are looking for an angle and we have the side on the top if we are looking for a side.

Cosine law: a^2=b^2+c^2-2bccosA

We use the cosine law if we cannot use Sine Law but it has to have at least two sides and an angle or three angles.

To use the cosine law and sine law, you plug in the given sides and angles and isolate what you are trying to find.

 

 

 

 

Week 16 – Numeracy Assessment

Posted on by shannonf2015

Last week, we have done some practice with the numeracy test. What I have learned from doing these practice questions was that when we do the written part, we have to be convincing and detailed in our explanation and that it’s not so much about which is the correct answer. It’s more about your reasoning. Another important method I have learned while doing these questions is that you should always think or write down your reasoning behind why you chose your answer even when it’s multiple choice.

In some practice questions, I have learned how to determine which graph represents the situation the best, as well as how to read a graph. When we did some questions that involved making our own plan, I learned it’s helpful to write down ideas in a chart to lay out my ideas clearly then explain each one in detail and why I chose that specific amount and choice. I also learned that keeping units is extremely important when doing these types of questions. For example, we did one question where we had to plan our water use to a certain amount of litres per week. It was helpful to draw out a chart so that I could put in my plan for the high-efficiency appliances and fixtures and do some adjustments on my plan if needed before started to do my explanation. I also remembered to keep the units in when I was writing my explanation when I kept referring to the chart.

Lastly, I have figured out that there can be more than one answer and that we should show all our work when doing calculations as it’s not as simple as typing in a bunch of numbers in the calculator. These questions makes you think more and you’ll have to analyse the information and images carefully. When I got stuck with a question that included calculations, I drew an image which helped me see the situation more clearly. We also had to do some other questions where they would give a list of different strategies a family decides to do in order to use less water and you would have to check off the ones that are unreasonable. Analysing each choice carefully and the chart given helped me eliminate choices and I was able to come to a conclusion on which one(s) were the least reasonable. I also tried to think if what they planned to do was even possible which also helped me.

Synthesis Essay – Meaning of Life

Posted on by shannonf2015

The Meaning of Life

 

Many people spend most of their lives trying to discover what to do with their valuable time which leads to the open-ended question: what is the meaning of life? The movie Dead Poets Society directed by Peter Weir takes place in 1959 in Vermont Boarding school Welton Academy. The story follows young boys who meet Mr. Keating, a young, passionate, and enthusiastic English teacher, who teaches them the values of thinking differently by finding their own voices while inspiring them to join the Dead Poets Society club. “The Secret Life of Walter Mitty” written by James Thurber is a short story set in the 1930s during the Great Depression. The story is based on Walter Mitty, an old man who fantasises in order to escape from reality to make his life more engaging. The movie Dead Poets Society and the short story “The Secret life of Walter Mitty”, both demonstrate different perspectives of life due to the obstacles being faced while finding a purpose. Todd and Neil from Dead Poets Society are encouraged by their English teacher to think freely to be able to discover themselves, whereas Walter Mitty retreats into his daydreams and imagines himself as a hero. In contrast, Todd and Neil are still youthful and are in search of a path unlike Walter Mitty who is trying to relive his past to escape his mundane life but continues to live freely through his dreams. Ultimately, both show the great significance of living life to the fullest while living under pressure, either by parents and society shown in Dead Poets Society or loved ones and society in “The Secret Life of Walter Mitty”.

To begin, each individual in both sources have different perspectives on the meaning of life because of their difference of age and morals, while being faced with different barriers they must overcome. Todd, the main character in Dead Poets Society is young, naïve, and shy. His fear of public speaking limits his ability of expression with also the pressure of his successful older brother weighing on him. The conflict between him and his mind telling him he is not good enough is discouraging, until Mr. Keating makes him do a “yawp” in front of the whole class. This “yawp” opens Todd up, leading up to the point where he has original poetry filled with passion seamlessly slip through his teeth. At this moment, Todd starts building up confidence and starts learning the importance of taking action in order to find his inner self that has been in hiding. Furthermore, Todd grasps Mr. Keating’s teachings and learns to contribute his own verse by jumping onto his desk and reciting “O Captain! My Captain!” (Weir) which is a reference to the poem they learned with Mr. Keating about Abraham Lincoln. Mr Keating wants to be called “Captain” in order to break the wall between teacher and father figure. The action of standing up shows that he is challenging traditional ideas and stereotypes in order to be free. He is saluting Mr. Keating to show that he understands his lessons, and that he has broken his shell and evolved into an independent young man. He learns to find his own voice and to stop letting the fear of getting expelled affect his opinion, opening his eyes to his true purpose. On the other hand, Walter Mitty tries to be a hero in his daydreams due to self regret. His fantasy world is out of the ordinary, absurd and filled with action and adventure. He lives under the pressure of society and his domineering wife but continues to make dull activities engaging and exciting. He also tries to open up to his wife about his feelings but gets rejected instantly: “’I was thinking’ said Walter Mitty. ‘Does it ever occur to you that I am sometimes thinking?’ She looked at him. ‘I’m going to take your temperature when I get home’ she said” (Thurber). Walter’s attempt of expressing his emotions to his wife shows that he sees his fantasies as not simply foolish dreams, but a secret life where he can escape to when needed. His words to his wife show that he still finds it important to make every day feel like a new day by facing new challenges, fears, and experiencing unforgettable adventures even in his head. Even though he cannot do many things physically, he still shows the relevance of keeping his inner adventurous and wild self. Therefore, both sources demonstrate how the difference of ages affects one’s viewpoints on the meaning of life.

Different sets of tones and moods are also used to spread their messages to the audience in order to effectively reach out to those that have been in search for their own purpose. In Dead Poets Society, Mr. Keating’s passion and personality shines through to inspire the audience to find their voices, making him come across as a father figure for many. He uses lots of poetry and literature to teach the values of expression and nonconformity. This effective usage of poetry inspires the audience to dig deeper into the meaning of life, and to take action in order to make one’s life exciting. When the Headmaster of Welton Academy talks about the four pillars of Welton to the students, they all stand up with synchronized voices: “’Gentlemen, what are the Four Pillars?’ ‘Tradition. Honor. Discipline. Excellence’” (Weir). This demonstrates the strict traditional system of rehearsing this belief to brainwash them into thinking the only way to success is to follow tradition and to work hard to get a good career. The boarding school already plans the student’s futures, giving them a limited guideline of how to live their lives rather than allowing the boys to choose their own path and to give them opportunities to discover themselves. In the “The Secret Life of Walter Mitty”, humor is used but because Walter’s character comes across as someone who is in desperate need of escaping reality, the mood comes across as sad and depressing. This tone and mood that the author uses makes it seem like the reader is making fun of him, as if he is pathetic, and just a regular old man who cannot do anything but simply dream. Additionally, the story is suspenseful and dramatic throughout the variety of fantasies to contrast his real life. The opening sentence, “’We’re going through!’ The commander’s voice was like thin ice breaking” (Thurber), tosses the reader into the middle of an action scene without any context to give the same immediate sense of reality to Walter’s fantasy life as is given to his real life. This usage of dialogue shows the complexity of Walter’s personality to show he feels free and alive in his dreams, and sometimes gets so involved he doesn’t know what is happening in his surroundings. Therefore, both sources share their messages by using different sets of moods and tones in order to effectively reach out to the reader and audience.

Lastly, both short story and movie teach valuable messages about the reasons of one’s existence and how to take action. Dead Poets Society teaches the importance of embracing your individualism and to make your lives extraordinary. Mr. Keating uses “carpe diem”, meaning seize the day, to inspire his students to look for opportunities and to make the most out of them. He teaches his students that young, timid men and women need to find their inner wild self to find the strength to be themselves. The dialogue between Neil and Mr. Keating also shows that young men need to connect with older men in order to find a mentor that will guide them through their life journey: “’Have you ever told your father what you told me? About your passion for acting? You ever show him that?’ ’I can’t.’ ‘Why not?’ ’I can’t talk to him this way’”(Weir). Neil feels more comfortable with Mr. Keating then his biological father, showing the importance of finding someone that will accept one’s decisions and opinions so that one may discover more about themselves. On the contrary, Walter Mitty’s message is about living life to the fullest before you feel regretful while also demonstrating the importance of not letting your age limit your capabilities. It’s better to try things then to not experience them at all, even if it may have a negative impact instead of regretting what it would be like. He continues to fantasize even when his wife does not support him. The symbolism of the last scene when Walter stands in front of a firing squad, represents him standing in front of the people that always harass him for dreaming: “He took one last drag on his cigarette and snapped it away. Then with the faint, fleeting smile playing about his lips, he faced the firing squad; erect and motionless, proud and disdainful, Walter Mitty the undefeated, inscrutable to the last” (Thurber). He stands in front proud and undefeated. This shows the relevance of sticking to one’s beliefs and dreams even if many disagree to show others the power of uniqueness and imagination which may soon help the breakage of stereotypes of old men. Based on both sources, they show the importance of taking action and to embrace your dreams in order to live a full life.

To conclude, Todd, Neil, and Walter show their own meaning of life and how they persevered through the difficulties of living under pressure. From the evidence shown, the boys in Dead Poets Society learn that their purpose is to find their own voices, and to diverge from being ordinary while also taking every opportunity. Walter Mitty learns that the purpose of life is to make life interesting, daring, and captivating, while keeping one’s adventurous side as one ages. Although each character discussed have their own definition of the meaning of life, they all learn that in order to find their purpose, they must be dauntless, brave, and speak out so that one may decide their own path, giving them the strength of ignoring the negative influences of others who limit their dreams and potential.

 

Works Cited

Dead Poets Society. Dir. Peter Weir. 1989. Film.

—. “The Secret Life of Walter Mitty.” The New Yorker 18 March 1939. Electronic.

 

Two things I did well: 

I was able to write a good opening with a strong hook and write a good thesis. I also used good transition words.

Two things I need to remember: 

To cut out deadwood to make my statements direct and to the point and making sure to explain in depth the quotes that I used in my essay.

 

 

 

 

 

Week 15 – Solving Rational Equations

Posted on by shannonf2015

This week I have learned how to solve when there is two fractions by cross multiplying and how to solve by finding the common denominator by factoring.

Let’s start with an example using cross multiplying:

 

First step is to write down the restrictions. The restriction is 2.

Next is to draw the butterfly, which is basically circle the numerator of one fraction with the denominator of the other fraction. Once you got those circled, those values circled together indicate that it will be multiplied together. Write them down making sure to keep the equal sign as you are solving. Now foil in the 3 in the brackets and isolate s. You get 2. Since we wrote down that the restriction of s cannot be 2, this is extraneous.

Let’s look at another example where we have to find the common denominator instead:

In this example, it looks too complicated to do cross multiplying. The first thing we should do is write down the restrictions which is x cannot be 0 or -1. Next, we can see in the first fraction, the denominator is factorable. We can take out a 2x and get 2x(x+1). By looking at both denominators of the fractions, the common denominator would be 2x(x+1) which allows us to cancel out the denominator of the first fraction, as well as the second fraction by multiplying both fractions with the common denominator. You will then have 2x(x-2) as the nominator for the second fraction which you will distribute the 2x in the bracket. Next, move the 6 over so you can factor. Start by finding out what is common which is 2 then start factoring. The answer is -1 or 3 but since we said the restriction is 0 and -1, -1 is not a solution; therefore, the answer is 3.

 

 

 

 

Week 14 – Rational Expressions

Posted on by shannonf2015

This week, I have learned what are non-permissible values and how to simplify rational expressions.

Non-permissible values are the values that x cannot be. The values are determined by the denominator; it’s the values that results in 0 as the denominator.

Let’s look at an example:

First step is to factor.

Once you factor everything out, list out the non-permissible values. After, you can simplify by crossing out what is common on the nominator and denominator which basically equals to one.

               

Let’s look at another example of multiplying and dividing rational expressions.

When it comes to dividing, we start by listing the given non-permissible values. The first one that we can see is 4.

Since it’s division, we must flip the second fraction (reciprocal) and then we can list the other non-permissible value which is 5. Next is to factor then list out any other given non-permissible values.

 

 

 

 

The other non-permissible value is -5. Now we can cancel out values diagonally which will give us the simplified expression.

 

 

 

 

 

 

 

 

Week 13 – Graphing Reciprocals

Posted on by shannonf2015

This week we have learned how to graph reciprocals for both linear functions and quadratic functions.

For graphing reciprocal functions, we have to determine the asymptotes.

The x-axis is a horizontal asymptote and a vertical asymptote is when x has a certain value, a vertical line that the graph approaches but never reaches.

For all reciprocal functions, y cannot be 0 since \frac{1}{f(x)} can never be 0.

When we take the reciprocal of a number, the only numbers that stay the same are -1 and 1. Therefore, when we graph, we find the points that line up to where y=1 and y=-1. These are the invariant points.

Let’s look at an example of a linear function.

\frac{1}{-3x+9}

First step is to graph the line.

Next is to locate the invariant points.

 

Next is to find the asymptotes. Horizontal asymptote is always y=0.

 

Once you have the line graphed, now you must draw a curved line that goes only through the variant points while approaching the asymptotes but not actually touching it.

 

let’s look at another example but with quadratic functions.

Example:

y = 2x^2-4x-6 and y = \frac{1}{2x^2-4x-6}

First is to graph the parabola. Start by factoring to find the x-intercepts.

 

 

Now that you have the x-intercepts, you can add them together and divide it by two to find the axis of symmetry and plug that and a point in standard form to find q for the vertex.

 

When you draw out the parabola, circle the invariant points and draw in the asymptotes.

Draw a curved line through the invariant points.

 

If the parabola has one x-intercept, then it will be divided into 4 zones and will have two invariant points:

 

If the parabola has no x-intercepts, then it will divided in two zones and it won’t have any invariant points or a vertical asymptote:

 

 

 

 

Spoken Word

Posted on by shannonf2015

The Problems of Being Short and Looking Young

“Do you need help sweetie?” “How old are you?” “Where’s your parents?”

I get these questions all the time, as if I’m a sixteen-year-old held captive by my child-self.  My toothpick arms make a rock climb for every toilet paper rack at supermarkets with adults swarming to help me. No free samples at Costco without my mother by my side in case I’m “lying” about my own allergies, or being shoved in the middle seat, squished like I’m an overused stress ball.

We short people live through the eyes of a five-year-old constantly looking up: either up people’s hairy nostrils, their moving jawline, or simply getting squished into our friends’ boobs. Our purpose is to be objectified as an armrest for those who are too lazy to balance on their own perfectly slim legs, stuffing up our noses with the noxious, stale stench of flies flying out their armpits. The lagging school days of lunging up the stairs leaves my legs crying in agony, and a thirty-minute walk turns to a thirty-minute power walk to keep up with my slender man legged friends.

To add on to these atrocities, I can’t even get a proper meal. Due to my baby face and minuscule hunched armadillo body, I’m instantly handed a kid’s menu. A KID’S MENU! Do I look like I’m 12? Despite my attempts of ordering from my mom’s menu, with direct eye contact and an obvious finger indication on the menu to the waiter, she brings me a fudging miniature sized burger. I did not live another four years for the same calories as my nine-year-old brother, thank you very much.

There’s also the daily struggle of having our view blocked by towering bodies and being shoved around like we’re in pinball. A day at the movie theater becomes dodge ball from the blocking of tall heads, large crowds becomes a stampede of rowdy sweaty bulls trampling on our ant bodies and standing in lineups turns us into waddling penguins.

Although it’s infuriating to be short and to look young, there are some advantages. For instance, I can get away with taxes, I have plenty of leg room on planes, and I get away from heavy duty work.

I am also skilled at hide and seek and getting piggyback rides.

But the unwanted tattoo I cannot remove is the term “cute”; it’s stitched in my skin. No “Hot” or “Beautiful” is ever puzzled together with my face. And no, I do not want to be referred to those, but the fact that I’m told “You’re so cute!” as my permanent so-called-compliment makes me want to gag.  I am not a baby, or a puppy, ok? And please don’t tell me to wear heels to solve my height issues; those unbearable human-made torture devices are unacceptable for my virgin feet.

Now being small does not always hide me.  Whenever it’s picture time, my spotlight shines, front and center, provoking my shy stomach. My teenage clothing sags like filled up trash bags and I must strain my husky words to be heard. Worst of all, 5th graders heights are either equivalent or greater than mine making me petrified of hyper children.

So before you treat me like a child, let me make things clear.  Yes, I am sixteen, yes, I am short, and yes, I do struggle. But hey, at least I get to save money by wearing kid’s clothing.

  1. Two things I did well

I was able to use lots of metaphors, imagery, and some similes throughout my writing, and I was able to present it quite well. I usually don’t do a rant because I find them quite difficult; however, I am proud I was able to take my experiences and make it into a piece of writing to share it with my short folks.

2. Two things I need to improve on

I need to improve on my speaking when I present, and be more insightful when I am writing. I found myself running out of breath a lot while I was presenting so I need to find a way to make sure I do enough pauses. I did talk faster when I was in front of the class as I was really nervous, so I need to find coping methods to help me calm down before I present. I also need to start going deeper into my writing and just improving my writing in general.

3. Obstacles I encountered and the solution

While I was writing this spoken word, I tried to think of different ways of explaining my emotions or how I see things using metaphors or other descriptive words but I found this quite hard. Luckily, I managed to think of some by writing down my ideas first then thinking of ways to express/ show them without simply telling them. I also am not good at rants and I was hesitant to do this but this feeling of being short and young really got to me so I decided to go for it. I did in the beginning struggle on how to rant as I do not know how to; however, I managed to by imagining myself ranting to those that treat me like a child. I am proud that I decided to do a rant this time and that I was able to do a decent job. I am also proud I was able to make some people laugh as I am not very funny.

Week 12 – Absolute Value Functions

Posted on by shannonf2015

This week, I have learned how to graph the absolute value of a linear function, the absolute value of a quadratic function and how to write it in piecewise notation.

Example of a linear function:

y = I3x-5I

Let’s start by graphing this.

We know the y-intercept is -5, and the slope is 3. Start by plotting the given information on the graph for y = 3x-5

Now, to be able to place the absolute value, we must remember that absolute values cannot be negative. So the line that goes past the x-axis will instead change to positive values which will make the line bounce upwards after touching the x-axis.

To write this in piecewise notation, we can’t really tell what the x-axis is here, so we can use the equation to determine the x-intercept.

 

 

Let’s look at an example of a quadratic function:

 

Let’s start by graphing this. We know the vertex is (-1, 1) and it’s congruent to y=x^2 which follows the pattern 1,3,5,7,9…

Once you have it graphed without the absolute value symbol, you now can start graphing the equation when it’s in the absolute symbol. To do this, all the negative values must switch to positive values. Therefore, the outsides of the parabola will flip up.


Now that you have this, we can use this graph to determine the intercepts and domain and range. The x-intercept is -2 and 0 and the y-intercept is 0. The domain is always the element of all real numbers (xER) and the range is y ≥ 0 as the values of y must be +.

To write this in piecewise notation, we must first look at the x-intercepts. We can see that the outer part changes but the inner part does not whether it’s in the absolute value symbol or not. So y = -(x+1)^2+1 is if  -2 ≥ x ≥ 0 (The inner part of the graph; we are including the + values and 0).

For y=-(-(x+1)^2+1) if x < -2 and x > 0 (The outer parts of the parabola; all the negative values).

So the piecewise notation is: