Graphs are pictorial representation of the characteristic behavior of mathematical functions. There can be numerous forms of graphical illustrations. 1st let us discuss about the functions of whose we sketch the graph. Function in a way is kind of relation that also has a set orderly pairs, but the difference between a relation and a function is that a function is always one – one & onto. For a relation to be one – one, every element in the domain set of the function must have a unique element in the range set. Onto means the complete domain of the function is covered. Depending upon the type of functions we deal with, the graph differs accordingly. For instance, suppose we have a linear function equation given as: h (x) = 7 x + 8, then the graph would represent a straight line. There can be other types of functions also like polynomial function, algebraic function, exponent function, logarithmic function etc. The types of graphs and the functions behaviors differ with the changing type of the functions. Suppose we have to graph the above linear function h (x) = 7x + 8, we would start by evaluating the domain of the function 1st. The domain in this case will be all real numbers and the corresponding range and therefore the coordinate pairs can be evaluated to plot the graph as follows: (0, 8), (-1, 1), (1, 15), (-2, -6) etc. Graph of the function can be drawn as follows:
Next we will discuss how to find the range of a function?
The range of a function can be evaluated by substituting the values of the domain of function like we did in the example we considered above to find out the coordinate pairs. These concepts are important from the perspective of iit jee syllabus.
Graphing Linear Functions 