# Increasing & Decreasing Functions

• Jan 19th 2007, 06:51 PM
symmetry
Increasing & Decreasing Functions
What is the difference between an increasing and decreasing function?
• Jan 19th 2007, 11:22 PM
CaptainBlack
Quote:

Originally Posted by symmetry
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
• Jan 20th 2007, 05:32 AM
symmetry
R

However, what does the upper case R mean?
• Jan 20th 2007, 07:26 AM
CaptainBlack
Quote:

Originally Posted by symmetry
It is the set of all real numbers. Often written $\mathbb{R}$.