Rational Functions Flashcards: Graphs & Asymptotes

Question 1

What is a rational function?

Accepted Answer

A function that can be written as $$f(x)=\frac{p(x)}{q(x)},$$ where $p(x)$ and $q(x)$ are polynomials and $q(x)
eq 0$.

Question 2

Find the vertical asymptotes of $f(x)=\frac{x+2}{x^2-9}$.

Accepted Answer

Factor denominator: $x^2-9=(x-3)(x+3)$. No cancellation, so vertical asymptotes are $x=3$ and $x=-3$.

Question 3

Find the slant asymptote of $f(x)=\frac{x^2+1}{x-1}$.

Accepted Answer

Divide: $$\frac{x^2+1}{x-1}=x+1+\frac{2}{x-1}.$$ Slant asymptote: $y=x+1$.

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