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

No Pressure, No Diamond…

Have you been practicing for the SAT? How do you solve this problem? What is the best way to approach this problem?

Everyone had been talking about the SAT even before the summer break started. In math class this year, we had been arduously allocated all the class time to prep ourselves for the upcoming SAT on October 6th, 2018.

The first three or four weeks of school was not an issue for any of the students until we got to the last two weeks, which nearly the test date, where pressures began to heighten up.

Personally, the most challenging part about SAT to me is the timing. I could say that I basically know almost all of the math contents in the test but the time’s pressure often made me missed some of the questions.

In order to approach this issue, I often set a limit time for myself for each question that I’ve been solving. Furthermore, when I looked at the question and when it seems to have a lot of text or complicated equation, I would quickly skip it and move on to the easier one; this way I am able to complete all the easy one first. Another strategy that I’ve been taking was to always leave at least 4 minutes of the full test to fill up the bubbles. For example, if I did the 38 questions with calculators one and I have 55 minutes, I would limit myself to use only 50 minutes in order to leave 5 minutes in filling the bubbles sheet.

Our math facilitator, Jeff Boucher, always keep telling us that the SAT is not the correct way to measure our capability but it is the stepping stone that we need in order to experience the abundant opportunities that the university offered. This is why it is important to us as the Cambodian change agent. 

“It’s not the size of the dog in the fight, it’s the size of the fight in the dog.” ― Mark Twain

Normal Distribution

AP Statistic contents encompass of many critical lessons and the normal distribution is one of them. Normal Distribution use to describe data that is symmetric (with a single peak) and follow the empirical rules (68-95-99.7). The empirical rules provide an estimate of the data spread using the mean and standard deviation. When the data follows the empirical rules, about 68% of the data is one standard deviation from the mean, 95% is two standard deviation from the mean, and 99.7% is three standard deviation from the mean. We can easily determine the data, whether it follows the empirical rules or not, through the normal curve. The area of the normal curves is always equal to 1. 


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