Question

Describe how to translate the graph of g(x)=ln x into the graph of f(x)=ln(-x)+5.

Answer 1

B. Reflect across the y-axis and translate 5 units up.

Step-by-step explanation:

The transformation of
`g(x)` into
`f(x)` is done by applying two steps:

1) Make a composition between
`g(x) = \ln x` and
`h(x) = -x` such that
`g'(x) = g \,\circ \, h\,(x)`. (Equivalent to a reflection across the y-axis)

`g'(x) = \ln (-x)`

2) Make a translation of the previous function of 5 units in the +y direction.

`h(x) = g'(x) + 5`

`h(x) = \ln (-x) + 5`

Hence, the right answer is B.