How to solve this behavior of log function question?

Question

(No calculator allowed)

Which interval correctly represents all values of x where f(x) = ln|x| is increasing?

A. (-infinity, -1] U [1, infinity)

B. (0, infinity)

C. (-infinity, 0) U (0, infinity)

D. [1, infinity)

Answer 1

f(x) = ln lxl

f is defined for all x except o

f'(x) = 1/x

When x < 0, f'(x) < 0. So, f is decreasing.

When x > 0, f'(x) > 0. So, f is increasing.

f is increasing on (0,∞).

Answer 2

b: (0, infinity)

undefined at x=0

decreasing for x<0

increasing when x>0

f(x) is an even function,

it reflects across the y axis

f(x)=f(-x)

check your answer with a graphing calculator