Final answer:
The graph of f(x) = 1/x + 5 varies from the graph of g(x) = 1/x by being shifted upward by 5 units, resulting in a new horizontal asymptote at y = 5.
Step-by-step explanation:
The graph of f(x) = \frac{1}{x} + 5 will differ from the graph of g(x) = \frac{1}{x} in a few key ways. First, let's review the graph of g(x), which is a classic example of a hyperbola. The hyperbola will approach two asymptotes: a vertical asymptote at x = 0 and a horizontal asymptote along the x-axis. Now, by adding 5 to the function g(x), we're effectively shifting the entire graph of g(x) up by 5 units on the y-axis. So the function f(x) will still have a vertical asymptote at x = 0, but the horizontal asymptote is now at y = 5. Thus, the graph of f(x) will look like the graph of g(x), but shifted upwards on the y-axis by 5 units.