Reflections of Exponential Functions — Quiz

Question 2 • Algebra: Concepts and Connections

Which graph represents a reflection of f of x is equal to 1 tenth times 10 to the x th power across the y -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 1).

Image with description On a coordinate plane, an exponential function increases from quadrant 3 to quadrant 4 and approaches y = 0. It goes through (negative 1, negative 1).

Image with description On a coordinate plane, an exponential function decreases from quadrant 2 to quadrant 1 and approaches y = 0 in quadrant 1. It goes through (negative 1, 1).

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, 1).

Explanation

Reflecting across the y-axis means replacing x with −x, so the reflected function is g(x) = (1/10)·10^(−x). It decreases as x increases, stays positive, and passes through (−1, 1), since g(−1) = (1/10)·10 = 1. As x moves right, the graph approaches y = 0, matching the graph that decreases from quadrant II into quadrant I.

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