Question

the graph of (f(x)=-2^{x}) is given below. write the equation of a function (g(x)) which would shift the graph of (f(x)) right 2 units and down 1 unit.

Explanation:

Step1: Apply horizontal - shift rule

For a function $y = f(x)$, shifting it $h$ units to the right gives $y=f(x - h)$. Here $h = 2$, so $f(x)$ becomes $f(x - 2)=-2^{x - 2}$.

Step2: Apply vertical - shift rule

For a function $y = f(x - h)$, shifting it $k$ units down gives $y=f(x - h)-k$. Here $k = 1$, so $g(x)=-2^{x - 2}-1$.

Answer:

$g(x)=-2^{x - 2}-1$