Graph the following piecewise function and then find the domain.

[6,9)
(-4,9)
(-4,9]
(6,9]

First, graph the parabola f(x)=3x²+1
this quadratic equation doesn't have x to the first power, so the symmetry line is the y axis. locate this five points: (0, 1), (1, 4), (-1, 4), (2, 13), (-2, 13).
connect them to make the parabola. 
I was going to set the last two points at (-4, 49) and (6, 109), but that would require two much space on paper.
You actually need these two points to do the graph right.
Put  a little hollow circle on each end of the parabola.

second, draw the graph for f(x)=6, which is a horizontal line segment parallel to the x axis, starting from 6 units above x=6, ending at 6 units above x=9. solid dots to cap both ends. 
the domain is the value of x. in this case, -4,x≤9, excluding -4 but including 9, the answer is C.