Question

HELP!!! URGENT!!! 40 POINTS!!!

Which of the following functions is represented by the graph?

Answer 1

`y=\log _{(1)/(4)}\left(x\right)`

Explanation:

The function that belong to the graph is the second one:

`y=\log _{(1)/(4)}\left(x\right)`

We deduct from the properties of logarithmic functions. When the base is between 0 and 1, the function will decrease, and 1 divided by 4 is in this interval, also the graph is showing a decrease. Therefore, the function with base
`(1)/(4)` is the answer.

However, we have to options, but one of them has a negative argument, which cannot represent the graph, because that negative means a reflection across y-axis, and the given graph is not reflected.

Therefore, the correct answer should your included a decrease behaviour, which is:

`y=\log _{(1)/(4)}\left(x\right)`

(Also, the actual graph is attached, you can see that's the same)