Respuesta :

TaeKwonDoIsDead

Answer:

D

Step-by-step 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 [tex]ln(5-x)[/tex] with the parent graph of [tex]lnx[/tex]. 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.

carlosego

Answer:

Option d

Step-by-step explanation:

Let f(x) be a logarithmic function of the form [tex]f(x) = log(x)[/tex]. So:

[tex]y = f(-x)[/tex] represents a reflection of f(x) on the y axis.

[tex]y = f(-x) = log(-x)[/tex]

Then:

[tex]y = f(x + 5)[/tex] represents a displacement of [tex]f(x)[/tex] 5 units to the left.

[tex]y = f(x + 5) = log(x + 5)[/tex]

Therefore, the operation:

[tex]y = f(-x + 5) = log(5-x)[/tex]

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

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