That is, there may be certain input values for x that cause the polynomial function in the denominator to output a zero. That is, zero times 8 is zero. This value for x also makes the denominator equal to zero. At the places where the function is undefined we say that the function is discontinuous. And we say that there are discontinuities in the function at the x-coordinates where it is undefined.
Discontinuities are locations for x values that make the function undefined.
Not all discontinuities in rational functions create vertical asymptotes, but these do. Some discontinuities are not asymptotic, but are removable. More about that later. Vertical asymptotes show up as vertical white lines on the above applet. Go ahead and try that .