1. The problem asks to describe the translation of the function $f(x) = \left(\frac{1}{2}\right)^x$ to the function $g(x)$ based on the graph. 2. The original function is $f(x) = \left(\frac{1}{2}\right)^x$, which is an exponential decay function. 3. The graph shows that $g(x)$ is the same shape as $f(x)$ but shifted vertically upwards. 4. A vertical translation of a function $f(x)$ by $k$ units up is given by: $$g(x) = f(x) + k$$ 5. The graph indicates that the horizontal asymptote of $g(x)$ is at $y=4$, while for $f(x)$ it is at $y=0$. 6. This means $g(x)$ is $4$ units above $f(x)$, so: $$g(x) = \left(\frac{1}{2}\right)^x + 4$$ 7. Therefore, the translation is a vertical shift of 4 units up. Final answer: The translation of $f(x)$ to $g(x)$ is a translation of four units up.