Drawing the graph of a function can be a very good idea to determine the roots of a function, which can be found by noting the values of the variable that make the value of the function equal to zero. This is especially important in cases where the function is of a higher degree and it is not possible to find the roots manually.
The use of graphs can also provide an approximate idea of the roots; this provides a way of verifying if the roots determined by other methods are right or not.
The graph of the function allows us to see the slope that is made by it and note how the values of the function are changed by changes in the value of the variable. So, we can determine things like is the value of the function directly or inversely related to the value of the variable, is the function defined for all values of the variable, etc.
A rational function is of the form y =f(x) = P(x)/Q(x), where P(x) and Q(x) are the polynomials.
A graph can help to solve a problem (a) dealing with rational function which is in the form of an equation and find the roots . Graph can give us the solution, where the graph intersects with x axis.( b) To find or estimate the value of the ordinate y = f(x) at x = a, we can use a graph. (c) The continuity of y = f(x) could be judged by a graph. The discontinuity points are those values of x for which denominator becomes zero. The graph can detect the infinite jumps in ordinates and points of discontiuity if any. (d) The graph helps easily to identify in which interval f(x) is increasing or decreasing, (d) The graph helps us to locate where the value of the function attains maximum and minimum. These are some of uses of the graph.
The graph has its demerits as well. The accuracy of the graph is always subject our choice of scale. We can not go for any abnormally small scale or very large scale. We have to choose suitable scale to fit the graph on a given location (usually paper).