How does the graph of the transformed function \( g(x)=-2 \log _{2}(x-5) \) compare to the graph of its parent function \( f(x)=\log _{2} x \) ? (1 point) The transformed function has been reflectéd over the \( x \)-axis, vertically stretched by a factor of 2 , and translated 5 units to the left. The transformed function has been reflected over the \( y \)-axis, vertically stretched by a factor of 2 , and translated 5 units to the left. The transformed function has been reflected over the \( x \)-axis, vertically stretched by a factor of 2 , and translated 5 . units to the right. The transformed function has been reflected over the \( y \)-axis, vertically stretched by a factor of 2 , and translated 5 units to the right.

The transformed function \( g(x) = -2 \log_2 (x - 5) \) has indeed been reflected over the \( x \)-axis, as indicated by the negative sign in front of the logarithm. Additionally, since there is a factor of 2 multiplying the logarithm, it undergoes a vertical stretch by a factor of 2. Lastly, the expression \( (x - 5) \) signifies a translation 5 units to the right, not to the left. To visualize these transformations clearly, imagine starting with the graph of \( f(x) = \log_2 x \). Reflect it over the \( x \)-axis, making all the y-values negative. Then stretch it vertically to make it steeper, and finally, shift the whole graph 5 units to the right, giving you the new transformed graph of \( g(x) \). This understanding helps you see how dramatic changes in a function's equation translate into visible shifts and flips in graphing.