What is the difference between an increasing and decreasing function?
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