#### Answer

All the members of the family of linear functions $f(x)= 1 + m(x+3)$ have the point $(-3,1)$ in common.

#### Work Step by Step

This commonality can be seen by graphing several members of the family and seeing that they intersect at $(-3,1)$.
Alternatively, two arbitrary values of $m$ could be chosen, such as $m=1$ and $m=0$, and two functions with those values can be equated together as follows:
$1 + 1(x+3) = 1+0(x+3)$
$1 + x + 3 = 1$
$x + 3 = 0$
$x = -3$
Which would result in $y=1$ when inputted into any member of the family of linear functions $f(x)= 1 + m(x+3)$. This may be harder to identify than simply graphing the functions, however.