Question

Which graph represents the function of f(x) 9x^2 + 9x - 18 / 3x + 6

Answer 1

Answer:

The graph in the attached figure

Step-by-step explanation:

we have

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

Remember that in a quotient, the denominator cannot be equal to zero

so

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

Simplify the expression

Using a graphing tool

The roots of the quadratic equation in the numerator are

x=-2 and x=1

so

$9x^{2}+9x-18=9(x+2)(x-1)$

Simplify the denominator

$3x+6=3(x+2)$

substitute in the original expression

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

Simplify

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

$f(x)=3x-3$

Is the equation of a line

The y-intercept is the point (0,-3) (value of the function when x is equal to zero)

The x-intercept is the point (1,0) (value of x when the value of the function is equal to zero)

Graph the line, but remember that the value of  x cannot be equal to -2

The graph in the attached figure