Question

which graph represents the function of ( f(x)=\frac{9 x^{2}-36}{3 x + 6} )?

Explanation:

Step1: Simplify the function

Factor numerator: $9x^2 - 36 = 9(x^2 - 4) = 9(x-2)(x+2)$
Factor denominator: $3x + 6 = 3(x + 2)$
Cancel common factor $(x+2)$ (x≠-2): $f(x) = \frac{9(x-2)(x+2)}{3(x+2)} = 3(x-2) = 3x - 6$

Step2: Find domain restriction

Denominator $3x+6=0$ when $x=-2$, so hole at $x=-2$.
Compute $f(-2)$ from simplified form: $3(-2)-6=-12$, so hole at $(-2,-12)$.

Step3: Check graph features

Simplified function is line $y=3x-6$ with hole at $(-2,-12)$. The first graph shows this line with a hole at $(-2,-12)$ (open circle there) and correct slope/intercept.

Answer:

The first graph (with open circle at (-2,-12) and line y=3x-6)