Answer:
The graph in the attached figure
Step-by-step explanation:
we have
[tex]f(x)=\frac{9x^{2}+9x-18}{3x+6}[/tex]
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
[tex]9x^{2}+9x-18=9(x+2)(x-1)[/tex]
Simplify the denominator
[tex]3x+6=3(x+2)[/tex]
substitute in the original expression
[tex]f(x)=\frac{9(x+2)(x-1)}{3(x+2)}[/tex]
Simplify
[tex]f(x)=3(x-1)[/tex]
[tex]f(x)=3x-3[/tex]
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
