Question

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

Please see pics for choices of answers:

Answer 1

The graph in the attached figure

Explanation:

we have

`f(x)=(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)=((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