Question

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

Answer 1

Answer:

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

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.