SOLUTION: I need help with graphing rational funtions. The question is...Identify the points of discontinuity,holes,vertical asymptotes, and horizontal asmyptotes of each. Then sketch the

Question 420081: I need help with graphing rational funtions.
The question is...Identify the points of discontinuity,holes,vertical asymptotes, and horizontal asmyptotes of each. Then sketch the graph.
#1... F(X)= - 4/x^2-3x
#2... f(x)= x-4/-4x-16
#3... f(x)= x+4/-2x-6
#4... f(x)= x^3-9x/3x^2-6x-9
#5... f(x)= 3/x-2
Please show me how to graph these equations.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Identify the points of discontinuity,holes,vertical asymptotes, and horizontal asmyptotes of each. Then sketch the graph.
#1... F(X)= - 4/x^2-3x
discont: x = 0 and x = 3
holes: none
vertical asympt : x = 0 and x = 3
horizontal asympt: 0x^2/x^2 = 0/1 = 0 : Ans: y = 0
------------------------------------------------------------
#2... f(x)= x-4/-4x-16
discont: x = -4
holes: none
v.a.:: x = -4
h.a.:: x/(-4x) = 1/-4 : ans y = -1/4
---------------------
#3... f(x)= x+4/-2x-6
discont: x = -3
holes: none
va:: x = -3
ha::x/-2x = -1/2: Ans: y = -1/2
--------------------------------
#4... f(x)= x^3-9x/3x^2-6x-9 = [x(x-3)(x+3)]/[3(x-3)(x+1)]
disc: x = -1
holes: x = 3
va: x = -1
ha: x^3/0x^3 = 1/0 = undefined : Ans: none
--------------------------------------------
#5... f(x)= 3/x-2
disc: x = 2
holes: none
va: x = 2
ha: 0x/x = 0/1 = 0 : Ans: y = 0
=====================================
Cheers,
Stan H.

RELATED QUESTIONS
Identify the points of discontinuity,holes,vertical asymptotes, and horizontal asmyptotes (answered by Edwin McCravy)

For each rational function, identify any holes or horizontal or vertical asymptotes of... (answered by stanbon)

hey i need help with this problem...... For each rational function, identify any holes (answered by checkley77,JSmall)

What are the points of discontinuity, holes, vertical asymptotes,x-intercept, and... (answered by stanbon)

PLEASE HELP ME WITH THIS QUESTION. I WILL BE VERY HAPPY.... (answered by rothauserc)

Please help me with this problem {{{y= (6x^2+x-2)/(3x^2+17x+10)}}} I need to describe... (answered by stanbon)

Find any points of discontinuity for the rational function. y=(x+3)(x-5)(x+7)/(x+1)(x+4) (answered by Boreal,Alan3354,rothauserc)

i need help with graphing rational functions with horizontal/vertical/slant asymptotes... (answered by jsmallt9)

find the rational fraction, identify any holes or horizontal or vertical asymptotes of... (answered by richard1234)