All About Nature Of Graph

Graph theory plays an important role in every branch of the vast mathematical sector. Numerous types of graphs deal with the structured representation of data. The eight main types of graphs are linear graph, power graph, quadratic graph, polynomial graph, rational graph, exponential graph, logarithmic graph, and sinusoidal graph. Every type can be visibly distinguished by observing the format and analysing the unique mathematical function on which the graph is based. It is worth noticing that the concept of graphs (as a predictive function) simplifies many complex and dynamic real-world systems by connecting the nodes.

The nature of line graph

A line graph is associated with a straight line and is drawn using the cartesian coordinate system. Simple line graphs are obtained from functions of the form y=mx+c, where m is the slope of the line (gradient), and c is the point where the line crosses the y-axis. It is called the y-intercept. It consists of one variable and two constants. The location and the nature of line graph of a particular linear function are determined by these data. If the value of m is positive, the line has an upward slope, and if the value of m is negative, the line has a downward slope. The graph shows the relation between two dynamic variables by connecting the nodes. Different line graphs are simple line graphs, multiple line graphs and compound line graphs. The multiple line nature of graph example is discussed below. 

The graph here shows the score achieved by four teams in two different periods. The data on the y-axis indicates the score. The data on the x-axis indicates the teams. The graph is a mixture of two simple line graphs. By analysing the graph, a comparison between the scores can be made. 

The nature of graph of quadratic equation

Quadratic graphs are obtained from the function in the equation y=px2+qx+r, where p, q, and r are the coefficients and x is the variable. The structure of such a graph is the parabola. The value of p, q, and r determines the location and the nature of graph of the quadratic equation. If the value of p is positive, the parabola will open upward. If the value of p is negative, it will open in a downward direction. The provided equation must have two real and unequal roots if the graph of the particular quadratic equation intersects the abscissa at two distinguished points. The provided equation must have two real and equal roots if the graph of the particular quadratic equation touches the abscissa at one point only. If the graph does not intersect the abscissa, the equation has no real roots. The nature of graph example is discussed below:

Here, the parabola intersects the x-axis at two distinct points. -1 and 2 are the roots of the given quadratic equation y=x2-x-2. The roots are real and unequal. By analysing such graphs, the properties of the function are determined. 

Conclusion

The nature of line graph and quadratic equation graphs have a large impact on the problem-solving ability of mathematics. It should be noted that the graphs of specific functions exhibit exceptional types of symmetry. The knowledge about symmetry can help in sketching graphs and observing information on them. The critical points, extrema, inflation points, stationary points, and discontinuities can be found in the graph. A particular problem’s end behaviour and starting behaviour can be judged from its graph. Graph theory is vital in showing trends, uncertainty and data forecasting.