Answer:
The graph in the attached figure
Step-by-step explanation:
we have
[tex]f(x)=\frac{9x^{2}-36}{3x+6}[/tex]
Remember that the denominator cannot be equal to zero
so
The value of x cannot be equal to x=-2
Simplify the numerator
[tex]9x^{2}-36=(3x+6)(3x-6)[/tex] ----> by difference of squares
substitute
[tex]f(x)=\frac{(3x+6)(3x-6)}{3x+6}[/tex]
simplify
[tex]f(x)=3x-6[/tex]
The domain is all real numbers except the value of x=-2
The y-intercept is the point (0,-6) ---> value of y when the value of x is equal to zero)
The x-intercept is the point (2,0) ---> value of x when the value of y is equal to zero)
therefore
The graph in the attached figure
