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The graph of \( g(x) \) is the reflection of \( f(x) \) across the x-axis. If \( f(x) = 3\left(\frac{1}{2}\right)^x \), the reflection across the x-axis will negate the expression. Therefore, the equation for \( g(x) \) is:

\[ g(x) = -3\left(\frac{1}{2}\right)^x \]

So, the correct option is:

\[ g(x) = -3\left(\frac{1}{2}\right)^x \]

The graph of f(x) and g(x) are shown below. The graph of g(x) is the reflection of the graph of f(x) across the x-axis. If f(x) = 3(1/2)^x, what is the equation of g(x)?

Discover how to determine the equation of g(x), which is the reflection of the exponential function f(x) = 3(1/2)^x across the x-axis. Includes detailed explanation of graph transformations and the formula g(x) = -f(x). Suitable for Grades 10-12.

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