How do you graph f(x)= (x^3+1)/(x^2-4)?

1 Answer
Jul 12, 2015

Graph of y=(x^3+1)/(x^2-4)
graph{(x^3+1)/(x^2-4) [-40, 40, -20,20]}

Explanation:

There is no secret to graph a function.

Make a table of value of f(x) and place points.
To be more accurate, take a smaller gap between two values of x

Better, combine with a sign table, and/or make a variation table of f(x). (depending on your level)



Before to start to draw, we can observe some things on f(x)
Key point of f(x):

Take a look to the denominator of the rational function : x^2-4

Remember, the denominator can't be equal to 0

Then we will be able to draw the graph, when :

x^2-4!=0 <=> (x-2)*(x+2)!=0 <=> x!=2 & x!=-2

We name the two straight lines x=2 and x=-2, vertical asymptotes of f(x), ie, that the curve of f(x) never crosses this lines.

Root of f(x) :

f(x)=0 <=> x^3+1=0<=>x=-1

Then :(-1,0) in C_f

Note : C_f is the representative curve of f(x) on the graph


N.B : J'ai hésité à te répondre en français, mais comme nous sommes sur un site anglophone, je prefère rester dans la langue de Shakespeare ;) Si tu as une question n'hésite pas!