Graphing Functions

In a function each input value is directly lined with one corresponding output value of that function. For example: If we have a relation that is defined by function rule f (s) = s², then it compares its input’s’ to its Square, both values are real. If we put input value as -8 then we get its output as 64. In function form we can also write it as: f (-8) = 64. Real number graph is indistinguishable for representation of a function. Representation of a graph is not applied for general function. General concept of a graph is characterized by graph of relation. A function is always recognized by its graph but they are not same because it happens that two Functions that have different value of co- domain must have same graph. If we test graph of a function then we use vertical line test and if we test whether function is one – to – one then we use horizontal line test. If we have Inverse Function then graph of inverse function can be obtained by plotting graph of function along the line q = p. (here 'p' is along x - axis and 'q' is along y – axis. In a graph a curve is one – to – one function if and only if it is a function. For example: Suppose we have a function:
 
F (x) = p, if p = 1,
            q, if p = 2,
            r, if p = 3. Then Graphing Functions of given values.
Here we get function value (1, p), (2, q), (3, r). We can also write function in cubical form as:
F (p) = p² – 9p, on plotting graph of this function, we get curve shown below:
 
This is how we plot functions on a graph.