Question

Describe the translation (Picture provided)

Answer 1

Option d

Explanation:

Let f(x) be a logarithmic function of the form
`f(x) = log(x)`. So:

`y = f(-x)` represents a reflection of f(x) on the y axis.

`y = f(-x) = log(-x)`

Then:

`y = f(x + 5)` represents a displacement of
`f(x)` 5 units to the left.

`y = f(x + 5) = log(x + 5)`

Therefore, the operation:

`y = f(-x + 5) = log(5-x)`

Represents a reflection on the y axis and a translation of 5 units to the left

Answer 2

D

Explanation:

We would need to understand 2 rules of translation in order to figure this out.

1. The graph of f(-x) is the graph of f(x) reflect about the y-axis

2. The graph of f(x+a) is the graph of f(x) shifted horizontally a units LEFT and the graph of f(x-a) is the graph of f(x) shifted horizontally a units RIGHT

We are comparing
`ln(5-x)` with the parent graph of
`lnx`. Firstly, there is -x in place of x, this means the graph is reflected about y-axis. Next, there is +5 added with -x, so it means the graph is shifted horizontally 5 units to the LEFT

Looking at the answer choices, D is the correct answer.