Precal Blog

First of all, i’m very sorry that this blog is being posted so late.  It may be a little irrelevant, seeing as fifth hour is in the middle of there exam right now, but hopefully this will help anyone who still needs to finish their portfolio =]

Rational functions were named because they consist of a ratio between two polynomials.  At the beginning of the year, the only thing that we learned was that these graphs were big and messy.  But today [well, actually a couple weeks ago] we learned how you really graph them.

When looking at rational functions, we have to look at both global and local behavior.  Global behavior includes horizontal and oblique asmptotes–what the graph will look like when we are zoomed out really far.  Global behavior is usually dependent on the leading coefficient.  Local behavior includes zeroes, y-intercepts, vertical asymptotes, and points of removable discontinuity.

Local Behavior:

X-intercept: This occurs when the numerator of the function equals zero.  These are also called the zeroes of the function.  The number of zeroes of the function (both real and nonreal) are equal to the degree of the leading coefficient.  If nonreal zeroes exist, they come in pairs.

Y-intercept: This occurs when x is equal to zero. Finding the y-intercept is simple–plug 0 in for x.  Most of the terms will equal zero, and you can solve the function realatively easily.

Vertical Asymptotes: These occur when the denominator of the function equals zero and the numerator does not.  On either side of the asymptote, the graph will get extremely close to this line, but it will never touch it.

Removable Discontinuity:  These occur when the function is in inderterminite form, 0/0.  Usually, when a function is equal to 0/0 both the numerator and the denominator can be factored.

Global Behavior:

Horizontal Asymptote:  If both the expression in the numerator and the expression in the denominator have the same degree, then as you zoom really far out, the function will look like a horizontal line.

Oblique Asymptote:  If they do not have the same degree, then as you zoom really far out it will look like a diagonal line.

Hope this helped guys, and again, i’m very sorry it’s so late =]

Well i was supposed to type up the questions of the class…but no one gave me any questions…so i guess i’m just going to write about what i’d like to review in class tomorrow! The one thing I’d really like to go over is learning target 35…I know we went over this in class and I have the ntoes for it..but i would just like to refresh my memory and make sure I’m not missing anything about how to derive it!  I don’t really know what else people have questions on, so I hope tomorrow we just brush up on all the learning targets and people can bring up the questions they didn’t have today, tomorrow!