Table of contents  
What is a Nonlinear Function?  
Nonlinear Function Table  
Nonlinear Function Equation  
Non linear Graphs  
Linear and Nonlinear Functions  
Nonlinear Function Examples 
A nonlinear function is a function whose graph is NOT a straight line. Its graph can be any curve other than a straight line. For example, if there are 100 fishes in a pond initially and they become double every week, then this situation can be modeled by the function f(x) = 100 (2)^{x}, where x is the number of weeks and f(x) is the number of fishes. Let us make a table and graph this function making use of the table.
Let's graph the table now.
The above graph is NOT a line and hence it represents a nonlinear function. From the above graph, we can say that the slope is not uniform on a nonlinear function. A nonlinear function can be described using a table of values, an equation, or a graph. Let us see each of them now. Some of the examples of non linear functions include quadratic functions, cubic functions, polynomial functions.
The steps to determine whether a table of values determine a linear function are:
Consider the following table of values.
Let us determine whether this table denotes a nonlinear function by using the steps mentioned above.
Since all the ratios of differences of y to the differences of x are NOT same, the function is a nonlinear function.
A linear function is of the form f(x) = ax + b. Since a nonlinear function is a function that is not a linear, its equation can be anything that is NOT of the form f(x) = ax+b. Some examples of nonlinear functions are:
Since a function that is NOT linear is being called as a nonlinear function, any function whose graph is NOT a straight line should represent a nonlinear function. In the following figure, all graphs represent nonlinear functions as they are NOT straight lines.
Here are the differences between linear and nonlinear functions.
Example: Does the following table represents a nonlinear function?
Sol: Yes.
The differences of every two successive values of x are 1, 1, 1, and 1.
The differences of every two successive values of y are 2500, 1250, 625, and 312.5.
Their corresponding ratios are 2500, 1250, 625, and 312.5, which are NOT the same.
Hence the function represented by the table is nonlinear.
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