Graph key features of functions, linear equations and linear Essay

Graph key features of functions, linear equations and linear inequalities - Essay Example nd of relation with either one-to-one or many-to-one correspondence between the values of ‘x’ in the domain and the matching values of ‘y’ in the range. Given a set of ordered pairs that define a function, each element ‘x’ in the domain is distinct and does not repeat in value when paired with an element ‘y’ in the range. Through a vertical line test, one may determine whether or not a relation is a function in a graph such that on running down a vertical line, the curve is hit only at a single point everywhere in the curve. In this manner, it may be claimed that a ‘linear equation’ is a function, but not all functions are linear in nature. Based on the aforementioned properties and definitions along with the examples shown, linear equation and function share the attribute of having one-to-one correspondence so that the independent variable ‘x’ can assume any value wherein no two or more values of ‘y’ correspond to a common value of ‘x’. The one-to-one relationship is strict in meaning for linear equations whereas functions take into account correspondence that is many-to-one in type considering equations that represent relations in quadratic and cubic forms. Besides linear equation, a function may also be modelled by nonlinear forms such as rational, polynomial, logarithmic, or exponential. Thus, all linear equations are functions but not all functions are linear equations. An equation of a vertical line is given by a constant relation x = c where ‘c’ is a constant value which means that ‘x’ domain stays at a single steady value at any value of ‘y’. An example of a vertical line equation would be x = 7 which is a straight line parallel with the y-axis and whose slope is ‘infinity’. A sketch of its graph would look