Answered

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

Verified Answer :

ferretgirl02

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:

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

Step-by-step explanation:

Consider the provided function.

\(f(x)=\frac{9x^2+9x-18}{3x+6}\)

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:

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

\(f(x)=\frac{9(x-1)(x+2)}{3(x+2)}\)

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

\(f(x)=3x-3\)

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

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