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What are the coordinates of the hole in the graph of the function?

f(x)=5x−20 / 2x2−5x−12

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

hole: ( 4   , 20/11 )

 

was kind of confused on what to do with the 5 so it may not be 20, im unsure.

 Sep 9, 2019
 #1
avatar+103858 
+3

5x -20                            5 ( x-4)                        5

____________   =   ____________   =      _______     (1)    

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

 

Note that since (x - 4)  is a factor in the numerator, we might guess that it is also a factor in the denominator.....knowing this....the denominator should be easy to factor

 

The hole occurs where   x - 4  =  0   ⇒   at   x  = 4

 

To  find the y coordinate , sub 4  back into (1)       ⇒        5                      5

                                                                                     ________   =    _____

                                                                                      2(4) + 3               11

 

So......the hole occurs at   (4, 5/11)

 

See the graph here : https://www.desmos.com/calculator/uf623od70z

 

 

cool cool cool

 Sep 9, 2019

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