Reflections of Exponential Functions — Quiz

Question 8 • Algebra: Concepts and Connections

Which graph is the result of reflecting f of x is equal to 1 fourth times 8 to the x th power across the y -axis and then 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 crosses the y-axis at (0, negative 0.25) and goes through (1, negative 2).

Image with description On a coordinate plane, an exponential function approaches y = 0 in quadrant 1 and increases in quadrant 2. It crosses the y-axis at (0, 0.25) and goes through (negative 1, 2).

Image with description On a coordinate plane, an exponential function approaches y = 0 in quadrant 2 and increases into quadrant 1. It goes through the y-axis at (0, 0.25) and goes through (1, 2).

Image with description On a coordinate plane, an exponential function increases in quadrant 3 into quadrant 4 and approaches y = 0. It goes through (negative 1, negative 2) and crosses the y-axis at (0, negative 0.25).

Explanation

Reflecting across the y-axis replaces x with −x, and reflecting across the x-axis multiplies the output by −1. The result is g(x) = −¼·8^(−x). It crosses the y-axis at (0, −0.25) and passes through (−1, −2); as x increases, its values rise toward 0 from below. This matches choice D.

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