Graph functions $f$ and $g$ in the same rectangular coordinate system. Graph and give the equations of all asymptotes.
$f(x)=\left(\frac{1}{2}\right)^{x}$ and $g(x)=\left(\frac{1}{2}\right)^{x-4}+2$

Graph $f(x)=\left(\frac{1}{2}\right)^{x}$ and $g(x)=\left(\frac{1}{2}\right)^{x-4}+2$ and their asymptotes. Graph the asymptotes as dashed lines. Use the graphing tool to graph the functions.

Step 1 ：Understand the functions $f(x)=\left(\frac{1}{2}\right)^{x}$ and $g(x)=\left(\frac{1}{2}\right)^{x-4}+2$. The first is an exponential decay function, and the second is a transformation of the first function.

Step 2 ：For $f(x)$, plot the point (0,1) and draw a curve that starts from the upper left, goes through this point, and approaches the x-axis as x increases. The x-axis (y=0) is the horizontal asymptote, which should be drawn as a dashed line.

Step 3 ：For $g(x)$, plot the point (4,1) and draw a curve that starts from the upper left, goes through this point, and approaches the line y=2 as x increases. The line y=2 is the horizontal asymptote, which should be drawn as a dashed line.

Step 4 ：Remember, the graphs of these functions never touch their asymptotes. They get infinitely close to them, but never cross them.