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

f(x)=5x−20 / 2x^{2}−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.

jjennylove Sep 9, 2019

#1**+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

CPhill Sep 9, 2019