Question

Medal!!!!
Describe the steps for graphing a rational function.

Answer 1

1. Find the roots of the denominator. These identify the locations of vertical asymptotes.
2. Find the roots of the numerator. These are places where the function will have a value of zero (x-intercepts).
3. Find the limit value or function as the independent variable (x) goes to +Infinity and as it goes to -Infinity. These identify horizontal (or slant) asymptotes.

Having done this, you have divided the graph into regions in which the function will be continuous, and you will have identified some specific points on the graph (the zeros, x-intercepts). If you need, you can look at the function's derivative to determine maxima or minima in the various regions, or you can choose some points in each region to evaluate and plot.

You can use a site such as Wolfram Alpha to give a clue as to features of the graph.

Answer 2

i need crisp answers

Answer 3

http://www.wolframalpha.com/

Answer 4

i told u how

Answer 5

http://www.wikihow.com/Graph-a-Rational-Function

Answer 6

i need short answer!!!!!
or please explain what u wrote

Answer 7

theres nothing short about it hun

Answer 8

the ans is too long...

Answer 9

i need a sentence or two.
thatsall.

Answer 10

u dont except messages :(

Answer 11

First, determine the asymptotes, then the behavior of the graph around the asymptotes. Next, determine the max and mins. Lastly, draw the graph completely.

Answer 12

oh. thanks

Answer 13

I would still prefer $w3g's answer because it's more detailed :)

Answer 14

yeah the matter was that i really needed a small answer.

Answer 15

alright, it's up to you. goodluck :)