Problem
Graph the function \[ f(x)=\left(\frac{1}{6}\right)^{x} \]
Solution
Step 1 ：First, we generate a range of x-values and calculate the corresponding y-values using the function \(f(x)=(\frac{1}{6})^{x}\).
Step 2 ：Then, we plot these points on a graph.
Step 3 ：The graph of the function \(f(x)=(\frac{1}{6})^{x}\) is a decreasing curve that approaches zero as \(x\) increases.
Step 4 ：The function is always positive and decreases rapidly for positive \(x\), but decreases more slowly for negative \(x\).
Step 5 ：The function never reaches zero, but gets arbitrarily close to zero as \(x\) goes to infinity.
Step 6 ：\(\boxed{\text{The graph of the function } f(x)=(\frac{1}{6})^{x} \text{ is a decreasing curve that approaches zero as } x \text{ increases.}}\)
