Answer:
The coordinates of the hole in the graph of the function f(x) are (3,∞).
Step-by-step explanation:
The given function is
[tex]f(x)=\frac{x^2-9}{x-3}[/tex]
Hole in the graph means the function is not defined at that point.
The graph of f(x) is not defined at that point where denominator equal to 0.
[tex]x-3=0[/tex]
[tex]x=3[/tex]
It means the function f(x) is not defined at x=3.
[tex]f(x)=\frac{x^2-3^2}{x-3}[/tex]
[tex]f(x)=\frac{(x+3)(x-3)}{x-3}[/tex]
Cancel out the common factor.
[tex]f(x)=x+3[/tex]
Therefore coordinates of the hole in the graph of the function f(x) are (3,∞).
