Answer
The graph of $g(x)$ is the graph of $f(x)$ moved left by 1 unit.
Work Step by Step
Observe:
$f(0)=6^0=1$ which gives the point: $(0,1) $
$g(-1)=6^{-1+1}=1$ which gives the point: $(-1,1)$
$f(1)=6^1=6$ which gives the point: $(1,6)$
$g(0)=6^{0+1}=6$ which gives the point: $(0,6)$
$f(2)=6^2=36$ which gives the point: $(2,36)$
$g(1)=6^{1+1}=36$ which gives the point: $(1,36)$