Chapter 8.4, Problem 46HP

To determine

To explain how the factor can be used to determine the vertical asymptote or point discontinuity of a rational function

Answer to Problem 46HP

The vertical asymptote or point discontinuity of a rational function is explained by the use of factor.

Explanation of Solution

Given information:

An algebraic function who’s both the numerator and denominator are polynomials is termed as rational function. The vertical asymptote of a rational function is found when the denominator is kept equal to zero and the point discontinuity is found when the common factor is eliminated from both numerator and denominator.

So whenever any rational function is given then factor its numerator and denominator completely. If there is a factor that cancels, then the $x$ value which makes that factor zero is point discontinuity. If there is a factor in the denominator that does not cancel, then the $x$ value which make the factor zero is a vertical asymptote.

Therefore, the vertical asymptote or point discontinuity of a rational function is explained by the use of factor.