The first piece of the function \( f(x) = x + 3 \) is defined for the interval \( 0 \leq x \leq 6 \). The last point graphed in this piece occurs at the right endpoint of the interval.
Therefore, to find the last point, we evaluate the function at \( x = 6 \):
\[ f(6) = 6 + 3 = 9 \]
Thus, the last point graphed on the first piece of the function is \( (6, 9) \).