1.What are the coordinates of the hole in the graph of the function f(x) ?

1.

 

\(f(x) = \dfrac{x^2+3x-28}{x+7}\\ f(x) = \dfrac{(x-4)(x+7)}{x+7}\)

The hole is on x = -7.

The required coordinates is \(\left(-7,\displaystyle\lim_{x\rightarrow -7}f(x)\right)\).

\(\displaystyle\lim_{x\rightarrow-7}f(x) = \lim_{x\rightarrow-7}(x-4) = -11\).

Therefore, the coordinate of the hole is \((-7,-11)\).

2.

 

The first option, which is the option on the top left corner.