Question

Describe how to transform the graph of g(x) - Inx in the graph of f(x) - In (-x)-9.

a. Reflect across the y-axis and translate 9 units to the left

b. Reflect across the x-axis and translate 9 units to the left

c. Reflect across the x-axis and translate 9 units to down

d. Reflect across the y-axis and translate 9 units to down

Answer 1

d. Reflect across the y-axis and translate 9 units to down

Explanation:

Reflection of the graph of a function across the y-axis is accomplished by replacing x with -x in the function definition.

Translation of the graph of a function by k units upward is accomplished by adding k to the function value.

Application

Here, we observe that f(x) is g(x) with x replaced by -x. That means the graph of f(x) will be the graph of g(x) reflected across the y-axis.

The function f(x) is the function g(x) with -9 added to it. That translates the graph downward by 9 units.

These transformations, reflection across the y-axis and translation 9 units downward, can be seen in the attached graphs. Corresponding points are marked.