Given the function f(x)=log

Question

8
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x, construct the function g(x) such that the graph of g(x) is the same as the graph of f(x) but shifted 7 units down, shrunk vertically by a factor of 15, and reflected across the y-axis.
In 1–2 sentences, describe the construction of the function and identify the correct function.

Answer 1

To construct the function \( g(x) \) from \( f(x) = \log_8 x \), we first reflect it across the y-axis, giving us \( f(-x) = \log_8(-x) \). Next, we vertically shrink it by a factor of 15 to obtain \( \frac{1}{15} \log_8(-x) \), and finally, we shift it down 7 units, resulting in \( g(x) = \frac{1}{15} \log_8(-x) - 7 \).

Thus, the function is \( g(x) = \frac{1}{15} \log_8(-x) - 7 \).