N/A — Exam

Question 36 • Mathematics I

Which graph represents a reflection of f of x is equal to 1 third times 9 to the x th power across the x -axis?

Answer

Image with description 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).

Image with description 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).

Image with description 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).

Image with description 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).

Explanation

Reflecting a graph across the x-axis changes each y-value to its opposite, so the reflected function is g(x) = −⅓·9ˣ. At x = 1, f(1) = ⅓·9 = 3, so the reflected graph passes through (1, −3). It stays below the x-axis, approaches y = 0 from below as x goes left, and falls as x increases, matching choice A, the graph in quadrants 3 and 4.

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