Graph of a function
The graph of a function is the set of all points whose co-ordinates (x, y) satisfy the function y = f(x). This means that for each x-value there is a corresponding y-value which is obtained when we substitute into the expression for f(x).
The domain of f is the collection of points on the x-axis such that the vertical line through these points meets the graph. The range of f is the collection of points on the y-axis such that the horizontal line through these points meets the graph.
Plotting the graph of a function
Since there is no limit to the possible number of points for the graph of the function, we will follow this procedure at first:
⇒ select a few values of x (both positive and negative values)
⇒ obtain the corresponding values of the function
⇒ plot these points by joining them with a smooth curve
Plot the graph of the function f(x) = x + 2.
The graph of the function y = x + 2 is a straight line. The graph of all linear functions will be a straight line.
Plot the graph of the function f(x) = (x + 1)1/2
For this function, y is not defined for values of x less than -1. Hence, x < -1 is not in the domain.
Graphs of standard functions