Question

which of the following transformations are used one transfer me the graph of the parent function F ( X )=log5X to the graph of G( X) = -2log 5( X -6)

Answer 1

To transform the graph of the parent function \(f(x) = \log_5(x)\) to the graph of \(g(x) = -2\log_5(x-6)\), the following transformations are used:
1. Vertical Reflection: The negative sign in front of the logarithm function reflects the graph vertically.
2. Vertical Stretch: The coefficient "-2" stretches the graph vertically by a factor of 2.
3. Horizontal Shift: The "-6" inside the logarithm function shifts the graph horizontally 6 units to the right.