given the function y=2-log(x) find domain, determine vertical asymptote and show work.

Answer 1

log is only defined for positive numbers. So,

domain is x > 0

You know what y = log(x) looks like. Vertical asymptote at x=0.

y = -log(x) is just log(x) reflected about the x-axis. Still has the vertical asymptote at x=0.

y = 2 - log(x) = -log(x) + 2 is just that graph shifted up 2 units. Asymptote does not change.