Question

Which graph represents the function of f(x) = the quantity of 9 x squared plus 9 x minus 18, all over 3 x plus 6?

graph of 3 x minus 3, with discontinuity at negative 2, negative 9
graph of 3 x minus 3, with discontinuity at 2, 3

Answer 1

f (x)= (9x^2+9x-18)/(3x+6)
because the denominator (3x+6) can't be equal to 0 there's going to be a discontinuity at x=-2
And that's enough information to determine that is graph of 3 x -3 with discontinuity at -2, -9

Answer 2

The correct option is A) graph of 3 x minus 3, with discontinuity at negative 2, negative 9.

Explanation:

Consider the provided function.

`f(x)=(9x^2+9x-18)/(3x+6)`

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:

`3x+6=0`

`x=-2`

Thus, the function is not defined at x = -2

The above function can be written as:

`f(x)=(9(x^2+x-2))/(3x+6)`

`f(x)=(9(x-1)(x+2))/(3(x+2))`

`f(x)=3(x-1)`

`f(x)=3x-3`

Therefore, the correct option is A) graph of 3 x minus 3, with discontinuity at negative 2, negative 9.