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Graph y=1/x

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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.

Graph of the function y=1/x
Graph of the function y=1/x

Some points on the graph of the function are:

XY = 1/XPoint = (X,Y)
41/4 = 0.25(4,0.25)
20.5(2,0.5)
11(1,1)
1/2 = 0.52(0.5,2)
-1-1(-1,-1)
-2-0.5(-2,-0,5)

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”.

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