Answer
$g(x)$ is a reflection of $f(x)$ about the origin, that is, $g(x)=-f(-x)$
Work Step by Step
Observe:
$f(0)=(\frac{7}{2})^0=1$ which gives the point: $(0,1)$
$g(0)=-(\frac{7}{2})^0=-1$ which gives the point: $(0,-1)$
$f(1)=(\frac{7}{2})^1=\frac{7}{2}$ which gives the point: $(1,\frac{7}{2})$
$g(-1)=-(\frac{7}{2})^{-(-1)}=-\frac{7}{2}$ which gives the point: $(-1,-\frac{7}{2})$
$f(2)=(\frac{7}{2})^2=\frac{49}{4}$ which gives the point: $(2,\frac{49}{4})$
$g(-2)=-(\frac{7}{2})^{-(-2)}=-\frac{49}{4}$ which gives the point: $(-2,-\frac{49}{4})$
