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avatar+1489 

What are the coordinates of the hole in the function?

f(x)=2x2−5x−12 / 3x2−11x−4

Enter your answer by filling in the boxes. Enter your answer as simplified fractions, as necessary.

hole: (     ,     )

 Sep 6, 2019
 #1
avatar+106536 
+2

f(x)  =   (2x^2 - 5x - 12) / ( 3x^2 -11x - 4)

 

Factor the top/bottom ......one thing that might make this easier is to note that we probably have like linear factors on top/bottom

 

(2x^2 - 5x - 12)                ( 2x  + 3) ( x - 4)             (2x + 3)

_____________ =           ______________  =      _______       (1)

3x^2 - 11x - 4                     (3x + 1)( x - 4)              (3x + 1)

 

The x value where the "hole" occurs  where the like linear factors  =   0   .....so....   

 

x - 4  = 0

 

x  = 4

 

The y value of the coordinate is found by putting the x value into (1) =   [ 2(4)+3]  / [  3(4) + 1]  = 11/ 13

 

So....the "hole"  is at   (4, 11/13)

 

 

cool cool cool

 Sep 6, 2019
edited by CPhill  Sep 6, 2019
 #4
avatar+1489 
+1

I forgot to include my answer, but that is what I had wrote  for the answer. Awesome! Just wanted to double check my answer smiley. Gonna make some more notes of your explnatation ,thanks.

jjennylove  Sep 6, 2019
 #2
avatar+19934 
0

Deleted.....see Chris answer......

 Sep 6, 2019
edited by ElectricPavlov  Sep 6, 2019
edited by ElectricPavlov  Sep 6, 2019
edited by ElectricPavlov  Sep 6, 2019
 #3
avatar+19934 
0

 see above

ElectricPavlov  Sep 6, 2019
edited by ElectricPavlov  Sep 6, 2019

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