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.
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:
Furthermore, 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:
The 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.
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:
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:
- First open your MATLAB software for desktop
2. Type this lines in the command window: