f(x) = $a^x$: if a > 1, function is strictly increasing ($a^x$ > $a^y$ iff x > y). If 0 < a < 1, function is strictly decreasing ($a^x$ > $a^y$ iff x < y). Key property: $a^x$ > 0 for all real x — the exponential function never takes zero or negative values. This means equations like 2^x = -3 have no solution. The graph always passes through (0,1) and has the x-axis as a horizontal asymptote.