Question

Which graph represents the function of f(x) 9x^2 -36 / 3x + 6

Answer 1

Answer:

The graph in the attached figure

Step-by-step explanation:

we have

$f(x)=\frac{9x^{2}-36}{3x+6}$

Remember that the denominator cannot be equal to zero

so

The value of x cannot be equal to x=-2

Simplify the numerator

$9x^{2}-36=(3x+6)(3x-6)$ ----> by difference of squares

substitute

$f(x)=\frac{(3x+6)(3x-6)}{3x+6}$

simplify

$f(x)=3x-6$

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