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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
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#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.
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