Which statement best describes a method that can be used to sketch the graph. y = |x| - 2 a. translate the graph of y = |x| two units down. b. translate the graph of y = |x| two units up. c. translate the graph of y = |x| two units left. d. translate the graph of y = |x| two units right.

The correct option is A. Translate the graph of y = |x| two units down.

Step-by-step explanation:

The given function is

                ....(1)

The transformation of an absolute function is defied as

        .... (2)

Where, a is horizontal shift and b is vertical shift.

If a>0, then y=|x| shifts a units left and if a<0, then y=|x| shifts a units right.

If b>0, then y=|x| shifts b units up and if b<0, then y=|x| shifts b units down.

On comparing (1) and (2), we get

Since b=-2<0, therefore the graph of y = |x| two units down. The correct option is A.

you didn't post any answer choices, so its not 100% clear what your teacher is looking for

however, log(15/7) is equivalent to log(15) - log(7)

i'm using the rule log(x/y) = log(x) - log(y)