Answer:
(5, 7)
Step-by-step explanation:
A hole is found in the graph of a rational function where numerator and denominator factors cancel each other.
The x-coordinate of the hole is the value of x that makes the factor zero. The y-coordinate of the hole is the value of the simplified function after the cancelled factors are removed. It is the limit of the function value as x approaches the hole location.
__
[tex]f(x)=\dfrac{x^2-3x-10}{x-5}=\dfrac{(x+2)(x-5)}{x-5}=x+2\qquad x\ne 5[/tex]
The hole is found at x = 5. The limit of the function value as x approaches 5 is 5+2 = 7. The coordinates of the hole are (5, 7).
