(514) Given the function $f(x)=\left(\frac{1}{2}\right)^{|x-2|}$. (1) Sketch its graph; (2) Identify its monotonic intervals from the graph; (3) Determine the value of $x$ for which $f(x)$ attains its extremum.
(1) Draw the graph of $y=f(x)=\left(\frac{1}{2}\right)^{|x-2|}$ as shown in Figure 4-7. (2) From the graph, we know that the increasing interval of the function is $(-\infty, 2]$, and the decreasing interval is $[2,+\infty)$. (3) When $x=2$, $f(x)$ reaches its maximum value of 1.
Figure 4-7