According to the publication I've been using and an on-line function-graphing website, the graph of the function f(x)=the square root of (minus x) starts at the origin and extends up and asymtotically left. The problem is that the axes of the graph represent real numbers, and you can't get a real number answer when taking the square root of a negative number. Please show step by step the logic involved in obtaining such a graph. I believe my sources to be reputable. Thank you.

The domain of your function includes all negative x-s and x=0 (-∞ < x ≤ 0)(negative x semi-axis). This fucntion doesn't have an asymptote, it trends to infinity in the left (second) quadrant of the coordinate plane. For any negative x -x is positive and you can take square root of it.

Your confusion comes from misperception of the function: -x doesn't mean you are dealing only with negative numbers: "x" can be negative itself, but -x means number (-1) multiplied by x, which makes -x positive.