Question

Which graph represents a reflection of f(x) = 6(0.5)x across the x-axis?

On a coorindate plane, an exponential function starts in quadrant 3 and increases and approaches y = 0 in quadrant 4. It crosses the y-axis at (0, 6) and goes through (1, negative 3).
On a coordinate plane, an exponential function approaches y = 0 in quadrant 2 and increases into quadrant 1. It goes through (1, 3) and crosses the y-axis at (0, 6).
On a coordinate plane, an exponential function approaches y = 0 in quadrant 3 and decreases into quadrant 4. It goes through (negative 1, negative 3) and crosses the y-axis at (0, negative 6).
On a coordinate plane, an exponential function decreases from quadrant 2 to quadrant 1 and approaches y = 0 in the first qudrant. It goes through the y-axis at (0, 6) and goes through (1, 3).

Answer 1

Reflecting across the x-axis multiplies the function by −1, so the new function is g(x) = −6(0.5)^x.

g(0) = −6, g(1) = −3. For x → ∞, g(x) → 0−; for x → −∞, g(x) → −∞. So the graph lies entirely below the x-axis, starts in quadrant III, increases toward the x-axis and enters quadrant IV, and passes through (0, −6) and (1, −3).

Thus pick the graph described as starting in quadrant 3, increasing and approaching y = 0 in quadrant 4, with y-intercept (0, −6) and point (1, −3) (the first description, correcting the y-intercept sign).