Previously you learned about functions, graph of functions. In this lesson, you will learn about some function types such as increasing functions, decreasing functions and constant functions. These concepts are explained with examples and graphs of the specific functions where ever necessary.
Increasing, Decreasing and Constant Functions
Functions are increasing, decreasing and constant when you plot the graph of the function in a coordinate system. Let’s define the meaning of these functions.
Increasing function
A function 
- if
- implies
Example:
Let 
| x | f(x) | (x, f(x)) |
| -1 | 2 | (-1, 2) |
| 0 | 1 | (0, 1) |
| 1 | 2 | (1, 2) |
| 2 | 5 | (2, 5) |
The graph of the function will look like the following.
In the above graph, the function is increasing between the interval of (0, 2).
The value of
The value of 
Therefore,
Decreasing Function
A function
- if
- implies
Example:
Consider a function 
Before plotting the graph, you need to find points for the graph of the function. A table of points is given below.
| x | f(x) | (x, f(x) |
| -2 | 4 | (-2, 4) |
| -1 | 1 | (-1, 1) |
| 0 | 0 | (0, 0) |
| 1 | 1 | (1, 1) |
| 2 | 4 | (2, 4) |
The graph of the parabola is given below.
In the above graph, the function is decreasing between the interval ( -2, 0).
The value of
The value of
Then
Constant Function
The function is a constant function in an interval for some
- if
- implies
This is simplest form of graph of a function and such a function is always a straight line on the coordinate system.
Let 
The graph of constant function is given below.
In the above graph of the constant function.
The value of
The value of
Therefore,
