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
a. graph of 3 x plus 6, with discontinuity at 2, 12
b. graph of 3 x plus 6, with discontinuity at negative 2, 0
c. graph of 3 x minus 3, with discontinuity at negative 2, negative 9
d. graph of 3 x minus 3, with discontinuity at 2, 3

The answer is the option C

graph of minus , with discontinuity at negative , negative

Step-by-step explanation:

we have

Simplify

Step 1

Convert to a factored form the numerator

Group terms that contain the same variable, and move the constant to the opposite side of the equation

Complete the square. Remember to balance the equation by adding the same constants to each side.

Rewrite as perfect squares

Square root both sides

so

Step 2

Simplify the function f(x)

The domain of the function f(x) is all real numbers except the number

Because the denominator can not be zero

 ------> with a discontinuity at

The discontinuity is at point

the answer in the attached figure

g = (2, 2)

step-by-step explanation:

given the ratio is 1 : 1 then f is the midpoint of eg

let the coordinates of g = (x, y)

using the midpoint formula

(0 + x) = 1 ( multiply both sides by 2 )

0 + x = 2 ⇒ x = 2

similarly

(4 + y) = 3 ( multiply both sides by 2 )

4 + y = 6 ( subtract 4 from both sides )

y = 2

coordinates of g = (2, 2)