Function is very basic in calculus, it is used to illustrate relationship between two or more variables. Before we learn about function we need to know about real numbers, as a type of number that is most used in the application of mathematics. Real number has decimal (unlike integer), and it consist of irrational and rational number.

1In calculus, to compare two real numbers or more we often use the number line that can represent the algebraic description


Function is a relation between input and the corresponding output, the input sometimes called variable and one function can consist more than 1 variable / input, for example:

3Furthermore, when defining a function it is necessary to know the range of the input value that can be defined in the function, this value is popularly called domain. There are some restrictions for domain specification, based on the function, for example:


Types of Functions

These are some of the important functions that often arise in real-life situations:

7Composition of Functions

1The input should be in the domain of its output for the composition to be valid and the result can be defined. Just follow the basic mathematics rule, there should be no division by zero and no root of negative number.

3For example:


Observing how a function is built up can be a big aid in graphing, we now examine the graph of function:



The same principles apply for vertical translation:


Algebra Operations on Exponent Function

There are some rules to handle the algebra operation of exponents, this may come in handy and perhaps you already memorize it:

6Usually, geometric representation with graph or plot of a function is a better way to find out the domain of the function. That’s why a picture worth a thousand words.

Thus, in order to simulate how to plot or graphing a function and analyzing the domain and also the trends itself, we are going to use computer software named MATLAB, here are the figures of how to do it:

    1. First open your MATLAB software for desktop


2. Type this lines in the command window:



cAfter you type the plot line the plot will be shown up. The plot line is a command to plot 2D or 3D of a function you have defined earlier. Happy trying.