Given the function f(x) = log_5(x) which of the following functions is the transformation of f(x) right 6 units, up 3 units, stretched vertically by a factor of 2and reflected across the axis? Option # g(x) = - 1/2 * log_5(x + 6) - 3 Option #2 g(x) = 2 * log_5(- x + 6) + 3 Option #3 g(x) = - 2 * log_5(x - 6) + 3 Option g(x) = - log_5(1/5 * x - 6) - 3
The correct option is g(x) = 2 * log_5(- x + 6) + 3.
This option accounts for:
1. Right 6 units shift: - x + 6
2. Up 3 units shift: + 3
3. Vertically stretched by a factor of 2: 2
4. Reflected across the axis: - in front of x
So the correct transformation function is g(x) = 2 * log_5(- x + 6) + 3.