Question

Which graph represents a reflection of f(x) = One-third(9)x across the x-axis?

On a coordinate plane, an exponential function approaches y = 0 in quadrant 2 and increases into quadrant 1. It goes through (1, 3) and increases to (1.25, 7).
On a coordinate plane, an exponential function approaches y = 0 in quadrant 1 and increases in quadrant 2. It goes through (negative 1, 3) and (negative 1.25, 7).
On a coordinate plane, an exponential function approaches y = 0 in quadrant 3 and decreases into quadrant 4. It goes through (1, negative 3) and (1.25, negative 7).
On a coordinate plane, an exponential function approaches y = 0 in quadrant 4 and decreases into quadrant 3. It goes through (negative 1, negative 3) and (negative 1.25, negative 7).

Answer 1

Reflecting f(x) = (1/3)·9^x across the x-axis gives g(x) = −(1/3)·9^x. All y-values become negative, so the curve lies below the x-axis, approaches y = 0 from below, and passes through (1, −3). That matches the third description: "approaches y = 0 in quadrant 3 and decreases into quadrant 4; goes through (1, −3) and (1.25, −7)."