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Math·Advanced Math·Nonlinear functions

hard

The graph of $y=f(x)+2$ is shown, where $f$ is defined by an equation of the form $f(x)=a(b{)}^x+c$. If $a$, $b$, and $c$ are integer constants and $c\le 0$, which equation could define $f$?

A

$f(x)=-5(3{)}^x$

B

$f(x)=-5(3{)}^x-1$

C

$f(x)=-5(3{)}^x-3$

D

$f(x)=-5(3{)}^x-5$