Question

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

Please see pics for choices of answers:

Answer 1

The graph in the attached figure

Explanation:

we have

`f(x)=(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)=(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