# Thread: Increasing & Decreasing Functions

1. ## Increasing & Decreasing Functions

What is the difference between an increasing and decreasing function?

2. 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

3. ## R

However, what does the upper case R mean?

4. Originally Posted by symmetry

However, what does the upper case R mean?
It is the set of all real numbers. Often written $\mathbb{R}$.

RonL