Rational Function | Precalculus

This year, after the SAT on Oct 6th, I started my precalculus lesson. One of the sections that we covered in this term is called the Rational Function.  If you didn’t know or forget what it is, it’s a function in the form of r(x) = P(x)/Q(x), where P and Q are both polynomials and have graph that look like the picture at your left.  It was quite difficult for me at first to graph this function but once I noticed the pattern, it was fairly easy and straightforward.

In order to graph this rational function:

  1. Factor the numerator and denominator
  2. Look for intercepts: x-intercept is equal to the zeros of the numerator and y-intercept is equal to C value of numerator divide denominator
  3. Find the vertical asymptotes by determine the zeros of the denominator
  4. Figure out the horizontal asymptote by using the rule below. 
  5. Sketch the graph
r(x)= (x-2)/(x^2-2x-8) 
==> (x-2)/(x-4)(x+2)
x-intercept: 2
y-intercept: 1/4
vertical asymptote: -2, 4
horizontal asymptote: 0
slant asymptote: none

We also learned about slant asymptote, where the degree of the numerator is one greater than the denominator. This also means that there will be no horizontal asymptote. We determined the slant asymptote by divide polynomials with each other and we did not obtain its remainder.  Example below!

r(x)= (x^3+8)/(x^2-x-2) 
==> (x^3+8)/(x-2)(x+1)
x-intercept: -2
y-intercept: -4
vertical asymptote: -1,2
horizontal asymptote: none
slant asymptote: y = x+1

Lesson Learned

Besides learning about steps that engineers take to identify problems, brainstorm/assess their ideas, evaluate their product requirement, and build their own prototype; we also looked at different fail engineering projects and evaluated them: Titanic, Tacoma bridge, the Hindenburg and etc. 

Tipping of the Titanic

Image result for titanic sink 1942Most of us might have already heard of this elegant ship that got struck by the iceberg and sank into the Atlantic ocean in 1942, which killed more than 1,500 people. The main reason which causes this largest ship to sink is that of its watertight compartments—which engineers believed could never flood ship—didn’t get sealed and had filled up with water; this led the ship to tilt to one side and eventually sink. 

The Toppling of the Tacoma Narrows Bridge

This bridge was built across Puget Sound in Washington. It was a strong, light, narrow, and very flexible. Due to the strong wind (42 mph) on November 7th, 1940, had caused this 2,800-foot (853-m) bridge into a series of torsional oscillations and eventually collapse. 

The Hindenburg Disaster 

The main lesson that we learned from these fail engineering projects is that when we design our product, we have to consider all the possibility that could affect our product and should always test it in the real environment. 

Story of Change

This post will update you about my school newspaper project that I posted last time: previous post link.

In the project, I am the writer and the editor of the “Story of Change” category, which spotlight any changes that occur in our school (75%) and the world (25%). The primary reason that I chose that category is that I love to observe and evaluate the impact that changes have effects on people and their surrounding environment as well as how it shapes people mindset on certain topics. My favorite article that I wrote so far is about the China Belt and Road Initiative. It was very interesting to have a deeper understanding of how this project will shape our world and how different country to react to it. Please check it out below! Please click on this link to check more inspirational and amazing articles. http://ligeredge.org

The Flowing Arteries and the Beating Heart of the Modern World?

The old saying of connectivity “All roads lead to Rome” may soon become “All roads lead to Beijing” in our contemporary world with China’s ambitious infrastructure project.

Continue reading “Story of Change”

S’more | Stoichiometry

Have you had s’more before? What was it like? Was it good? 

If you (like me) didn’t know what the heck it is,  it is an amazing campfire snack in North America (according to Google) but as a Cambodian, I had never heard of or taste it before. Yet, last week in my Chemistry class, we did a S’more Lab to further our understanding and knowledge about limiting reactants (and get to taste it for the first time). 

We were given Graham crackers (Gc), marshmallow (M), chocolate piece (Cp) to make our own s’more. During the lab, we were required to balance out the equation and figure out limiting and excess reactants as well as calculate the experimental and theoretical yield. I have such a great time with my team doing the lab, by the way. 

  2Gc + M  + 3CP → Gc2MCp3   

This lab, not only it’s a lot of fun, but it had helped me to better understand about experimental and theoretical yield since I wasn’t sure on how to apply it into real life. Overall, I had such an incredible time do the lab and be able to learn about limiting reactants and make our own s’more. Yum! Yum!

School Newspaper

Liger Edge is the name of my school newspaper that we just recently created this year. I’ve been meaning to join this project since the first time that our facilitator, Cara Shelton, introduced us to it. I feel like writing is the easiest way for me to communicate with people and that I love writing. I really hope that my articles could influence people to create change. So far, I’ve written four articles for this newspaper and we’re still fixing the website so we’ll be launching soon….Enjoy reading one of my article down below and don’t forget to check out our website: http://ligeredge.org/

On Your Mark, Get Set,…GO?

What is a university like? How difficult will it be? How am I supposed to know which university will fit for me? What do I need to do to prepare for it?

Many students that plan to go to university are often troubled by these kinds of questions for the last two years of their high school. They do not know how to better train themselves to be ready for the upcoming marathon—college—without getting sidetracked or without someone there to coach them along the way.

Nevertheless, the Liger Leadership Academy (LLA) has already worked out a way for their senior cohorts students to get into shape. They basically let their students simulate the college experience itself by creating and managing their own individual school schedule!

“I think it’s exciting to try and manage your own time,” Karen, the school’s college counselor said about the student schedule, “[the schedule] also shows how hard it is to motivate themselves to do work.”

Continue reading “School Newspaper”