The function is:
(9x^2 - 36)
f(x) = ---------------------
3x + 6
You can simplify that function to a linear function for all x for which 3x + 6 ≠ 0
=> x ≠ - 2.
So, for x ≠ - 2, you can do:
(9x^2 - 36)
f(x) = --------------------- =
3x + 6
9(x^2 - 4)
f(x) = ---------------------
3(x + 2)
3(x + 2)(x - 2)
f(x) = --------------------- = 3(x - 2) = 3x - 6
(x + 2)
So, the graph is a right line that intercepts the y-axis at - 6 and the x-axis at x = 2, excluding x = -2 as the function is not defined for x = -2. That is the second graph of the second picture.
