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Properties of Rational Functions
$\displaystyle {p}{\left({x}\right)}$ and $\displaystyle {q}{\left({x}\right)}$ are polynomials and $\displaystyle {q}{\left({x}\right)}$ is not equal to 0 Values of $\displaystyle {x}$ found by solving $\displaystyle {q}{\left({x}\right)}={0}$ are part of the Domain Values of $\displaystyle {x}$ found by solving $\displaystyle {q}{\left({x}\right)}={0}$ are NOT part of the Domain The Horizontal Asymptote is a guiding line for the function as the input values increase or decrease without bound $\displaystyle {f{{\left({x}\right)}}}$ will have Vertical Asymptotes at all input values where $\displaystyle {f{{\left({x}\right)}}}={0}$

Properties of Rational Functions

Given the Rational Function $\displaystyle {f{{\left({x}\right)}}}=\frac{{{p}{\left({x}\right)}}}{{{q}{\left({x}\right)}}}$ , which of the following statements are true? Check all that apply.

$\displaystyle {p}{\left({x}\right)}$ and $\displaystyle {q}{\left({x}\right)}$ are polynomials and $\displaystyle {q}{\left({x}\right)}$ is not equal to 0
Values of $\displaystyle {x}$ found by solving $\displaystyle {q}{\left({x}\right)}={0}$ are part of the Domain
Values of $\displaystyle {x}$ found by solving $\displaystyle {q}{\left({x}\right)}={0}$ are NOT part of the Domain
The Horizontal Asymptote is a guiding line for the function as the input values increase or decrease without bound
$\displaystyle {f{{\left({x}\right)}}}$ will have Vertical Asymptotes at all input values where $\displaystyle {f{{\left({x}\right)}}}={0}$

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