Rational Function

Hi there!!! We meet again. I am not in the mood to write something. So just enjoy this video about rational function.

Upps... sorry I cannot find any video that are related to our syllabus, this is because rational functions is so wide thus the video i found talks about reciprocal, not what we learn in this chapter. But this video up there is a portion of what we learn in class. So I have no choice and just have to write it.


The general equation for rational functions is f(x)=ax+b/cx+d {a,b,c and d E R}.So i will demonstrate to you the key features of the function using the a,b,c and d term.

• Domain - {x E R, x cannot equal to -d/c}
• Range - { y E R, y cannot equal to a/c}
• x-intercept - x equal to -b/a.
• y-intercept - y equal to b/d.
• vertical asymptote - x equal to -d/c.
• horizontal aymptote - y equal to a/c.
• restriction - x cannot equal to -d/c.

How to find horizontal and vertical asymptotes manually?

1. Horizontal asymptote

• We have to substitute x negative infinity and positive infinity into the equation.
• and see the y values approaches what value, that value is the horizontal asymptote.
• or even easier just divide all the term in the equation with the x term with the highest degree

2. Vertical asymptote.

• To find the vertical asymptote we have to substitute the closest value of the restriction from the left and from the right. 
• The result must approaches negative and positive infinity. If not the restriction is not the horizontal asymptote.

HUH!!! Is that how to find the vertical and horizontal asymptote?? YES!! That's the way. In case if there are a question about how to find the VA and HA and required to show the solution, just use the method above. I think that all for now. See you next time!! bye!!