1. A function f(x) on the real line is increasing if:

for all x, y in R, such that if x>y, then f(x)>=f(y).

2. A function f(x) on the real line is strictly increasing if:

for all x, y in R, such that if x>y, then f(x)>f(y).

3. A function f(x) on the real line is decreasing if:

for all x, y in R, such that if x>y, then f(x)<=f(y).

3. A function f(x) on the real line is strictly decreasing if:

for all x, y in R, such that if x>y, then f(x)<f(y).

1a. A function f(x) on an interval I of the real line is increasing if:

for all x, y in I, such that if x>y, then f(x)>=f(y).

2a. A function f(x) on an interval I of the real line is strictly increasing if:

for all x, y in I, such that if x>y, then f(x)>f(y).

3a. A function f(x) on an interval I of the real line is decreasing if:

for all x, y in I, such that if x>y, then f(x)<=f(y).

3a. A function f(x) on an interval of the real line is strictly decreasing if:

for all x, y in I, such that if x>y, then f(x)<f(y).

RonL