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Graph the function $f(x)=\log _{2}(-x)+4$ on the axes below. You must plot the asymptote and any two points with integer coordinates.
Asymptote:

Step 1 ：The function given is a logarithmic function. The general form of a logarithmic function is \(f(x) = log_b(x-h) + k\), where \(b\) is the base of the logarithm, \(h\) is the horizontal shift, and \(k\) is the vertical shift. The asymptote of a logarithmic function is the vertical line \(x = h\). In this case, the function is \(f(x) = log_2(-x) + 4\), so there is a reflection about the y-axis (because of the negative sign in front of \(x\)), and the asymptote is \(x = 0\).

Step 2 ：The graph of the function is a reflection of the graph of \(f(x)=log _{2}(x)+4\) about the y-axis, and it is shifted 4 units upwards.

Step 3 ：Two points with integer coordinates on the graph are (-1, 5) and (-2, 4).

Step 4 ：\(\boxed{\text{Final Answer: The asymptote of the function } f(x)=log _{2}(-x)+4 \text{ is } x=0.}\)