the graph shows f(x) = (1/2)^x and its translation, g(x). which describes the translation of f(x) to g(x)…

Explanation:

Step1: Recall translation rules

Vertical translation: $y = f(x)+k$ moves $f(x)$ up ($k>0$) or down ($k < 0$) by $|k|$ units. Horizontal translation: $y=f(x - h)$ moves $f(x)$ right ($h>0$) or left ($h < 0$) by $|h|$ units.

Step2: Analyze the graph

The $y$-intercept of $f(x)=\left(\frac{1}{2}\right)^x$ is at $(0, 1)$ (when $x = 0$, $y=1$). The $y$-intercept of $g(x)$ is at $(0,5)$. The value of $y$ for $g(x)$ is 4 units greater than the value of $y$ for $f(x)$ at $x = 0$. And the shape of the curve is not shifted horizontally. So it is a vertical - shift.

Answer:

translation of four units up