Answer:
The correct option is A) graph of 3 x minus 3, with discontinuity at negative 2, negative 9.
Step-by-step explanation:
Consider the provided function.
[tex]f(x)=\frac{9x^2+9x-18}{3x+6}[/tex]
The above function is a rational function and the rational functions are defined everywhere except the zeros of the denominator.
Now find the zeros of the denominator:
[tex]3x+6=0[/tex]
[tex]x=-2[/tex]
Thus, the function is not defined at x = -2
The above function can be written as:
[tex]f(x)=\frac{9(x^2+x-2)}{3x+6}[/tex]
[tex]f(x)=\frac{9(x-1)(x+2)}{3(x+2)}[/tex]
[tex]f(x)=3(x-1)[/tex]
[tex]f(x)=3x-3[/tex]
Therefore, the correct option is A) graph of 3 x minus 3, with discontinuity at negative 2, negative 9.
