Question

given the function f(x)=logdown7 x, which of the following functions is the transformation of f(x) 9 units down, 5 units left, reflected across the x axis, and stretched vertically by a factor of 8?

Answer 1

Apply each change to y = log_7(x):

- Horizontal shift left 5: replace x by x+5 -> log_7(x+5)
- Vertical stretch by 8 and reflection across x-axis: multiply by -8 -> -8 log_7(x+5)
- Shift down 9: subtract 9 -> -8 log_7(x+5) - 9

So the transformed function is y = -8 log_7(x+5) - 9 (domain x > -5).