Prove that the function f(x) = log_e x is increasing on (0, ∞).

Prove that the function f(x) = log_a x is increasing on (0, ∞) if a > 1 and decresing on (0, ∞), if 0 < a < 1.

Prove that f(x) = ax + b, where a, b are constants and a > 0 is an increasing function on R.

Prove that f(x) = ax + b, where a, b are constants and a < 0 is a decreasing function on R.

Show that is a decreasing function on (0, ∞).

Show that decreases in the interval [0, ∞) and increases in the interval (-∞, 0].

Show that is neither increasing nor decreasing on R.

Without using the derivative, show that the function f(x) = | x | is

A. strictly increasing in (0, ∞)

B. strictly decreasing in (-∞, 0).

Without using the derivative show that the function f(x) = 7x - 3 is strictly increasing function on R.