Polynomials and Rational Functions

[happysmiler07]

If the rational function R has a vertical asymptote at x=4, then x-4 must be present in the denominator of R.

Explain why.

 

[stapel]

If the rational function R has a vertical asymptote at x=4, then x-4 must be present in the denominator of R.

Explain why.

What is the rule for vertical asymptotes? How do you find them from the rational functions?

 

[Bob Brown MSEE]

If the rational function R has a vertical asymptote at x=4, then x-4 must be present in the denominator of R.

Explain why.

If there is an asymptote at x=4 then f(x) must go to infinity at x=4.
A way to make a function infinite at x=4, is to divide by zero when x=4.
f(x)/(x-4) does that.

This is why you find x-4 in the denominator of a rational function when it has a vertical asymptote at x=4.

In R(x), to explain why x-4 specificly, notice that the numerator and denominator can be factored COMPLETELY into binomials (see definition of rational function)