Find the coordinates of the hole in the graph for the given function:
(2x^2+11x+12) / (x^2+7x+12)
This is online homework and my answer was a hole at (-3,5), however the website says it is wrong. Can anyone find my mistake? This is my work:
I factored out the equation to get: (x+8)(x+3) / (x+4)(x+3)
x+3=0 so x= -3
Cancel out the (x+3) on top and bottom so the equation now looks like: (x+8) / (x+4)
Then substitute -3 in for x: (-3+8) / (-3+4)=5
(2x^2+11x+12) / (x^2+7x+12)
This is online homework and my answer was a hole at (-3,5), however the website says it is wrong. Can anyone find my mistake? This is my work:
I factored out the equation to get: (x+8)(x+3) / (x+4)(x+3)
x+3=0 so x= -3
Cancel out the (x+3) on top and bottom so the equation now looks like: (x+8) / (x+4)
Then substitute -3 in for x: (-3+8) / (-3+4)=5
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You've just mis-factored the numerator.
(2x^2+11x+12) / (x^2+7x+12)
= (x+4)(2x+3) / (x+3)(x+4)
The "hole in the graph" is where (x+4) = 0 (so that the function is undefined 0/0).
So x = -4, and y = (2*-4 + 3)/(-4 + 3) = -5/-1 = 5
The "hole" is at (-4,5).
(2x^2+11x+12) / (x^2+7x+12)
= (x+4)(2x+3) / (x+3)(x+4)
The "hole in the graph" is where (x+4) = 0 (so that the function is undefined 0/0).
So x = -4, and y = (2*-4 + 3)/(-4 + 3) = -5/-1 = 5
The "hole" is at (-4,5).