The function \( f(x)=\left(\frac{1}{5}\right)^{x} \) is translated up 4 units. Which equation represents the translated function? \( g(x)=\left(\frac{1}{5}\right)^{x-4} \) \( g(x)=\left(\frac{1}{5}\right)^{x+4} \) \( g(x)=\left(\frac{1}{5}\right)^{x}+4 \) \( g(x)=\left[\frac{1}{5}\right)^{x}-4 \)

When you translate a function upward by a certain number of units, you simply add that number to the entire function. In this case, you start with \( f(x) = \left(\frac{1}{5}\right)^{x} \) and translate it up 4 units, resulting in \( g(x) = \left(\frac{1}{5}\right)^{x} + 4 \). So, the correct representation of the translated function is \( g(x)=\left(\frac{1}{5}\right)^{x}+4 \). As a fun fact, the process of translating functions is often graphically represented on a coordinate plane. Imagine lifting your favorite ice cream cone to enjoy it more—you just raise it up without changing its flavor or shape! That's what happens with function translations. Another interesting point is that the concept of translating functions is applicable in various fields, such as physics when analyzing the displacement of objects or in economics when adjusting curves to reflect new data. Engaging with these applications can make math feel much more relevant and exciting!