Subjects algebra

Function Reflection 05998C

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1. The problem asks how the functions $f(x) = 0.7 \times 6^x$ and $g(x) = 0.7 \times 6^{-x}$ are related. 2. Recall that reflecting a function $f(x)$ over the y-axis means replacing $x$ by $-x$ in the function, resulting in $f(-x)$. 3. Here, $g(x) = 0.7 \times 6^{-x}$ is exactly $f(-x)$ because $f(-x) = 0.7 \times 6^{-x}$. 4. Therefore, $g(x)$ is the reflection of $f(x)$ over the y-axis. 5. This means the graph of $g(x)$ is the mirror image of the graph of $f(x)$ when flipped across the y-axis. Final answer: $g(x)$ is the reflection of $f(x)$ over the y-axis.