The graph of the function y=1/x consists of two pieces. As the value of x approaches infinity we see that y tends more and more towards 0. Similarly, for large values of y, the value of x is very small and approaches closer and closer towards zero.
Some points on the graph of the function are:
|X||Y = 1/X||Point = (X,Y)|
|4||1/4 = 0.25||(4,0.25)|
|1/2 = 0.5||2||(0.5,2)|
The x-axis and the y-axis are known as the “asymptotes” for the graph. This is because the graph of the function slowly approaches closer and closer to the x-axis and the y-axis but never actually touches the x-axis or the y-axis.
The graph is symmetric about the origin and the two “pieces” of the graph are mirror images of each other. The shape of the graph is called a “rectangular hyperbola”.