Demo of the reciprocal function y=1/x

Simple plot of the reciprocal function . The domain (allowable x-values) are real numbers, but not x=0. The range of the function (y-values) are all real numbers but not y=0. Use the checkboxes to switch on/off a trace of points and the function curve.
Why does the y-value get so big? What happens when x approaches zero? What difference does approaching zero from the left or right make? Can the point on the curve ever touch the x-axis?