## Defined Graphs of Algebraic Functions

If f is a real-valued function of a real numbers, then the graph of f in the **xy**-plane is defined to be the graph of equation **y = f(x)**. The graph of a function f is the set of point **{ (x, y)| y = f(x), x **is in thedomain of f } in the cartesian plan for which (x, y) is an ordered pair of** f**.

The graph provides a visual technique for determining whether the set of points represents a function or not. if a vertical line intersects a graph in more than one point, it is not the graph of a function.

*Explain is given in the figure.*

### Sketch the Graph of a function

**A function Graph**

**Is Also a Function Graph**

**The Sketch is not a function **

### Best Method to Draw the graph

To draw the graph of y = f(x), we give arbitrary value of our choice to x and find the corresponding values of y. In this way we get ordered pairs \left(x_1\;,\;y_1\right) , \left(x_2\;,\;y_2\right) , \left(x_3\;,\;y_3\right) etc. These orders pairs represent points of the graph in the cartesian. We have these points and join them together to get the graph of the function.