Rational Functions and Complex Numbers Flashcards

A set of vocabulary flashcards covering the properties of rational functions, fractional operations, and introductory complex numbers based on lecture notes.

Holes

Created by the shared factors from the numerator and denominator in $y = \frac{p(x)}{q(x)}$.

X-intercepts

Created by the factors from the numerator in $y = \frac{p(x)}{q(x)}$.

Vertical Asymptotes

Created by the factors from the denominator in $y = \frac{p(x)}{q(x)}$.

Horizontal Asymptotes

Found from the ratio of the leading terms of the rational function.

Undefined values (domain restrictions)

Occur when the denominator of a rational function $= 0$ because you cannot divide by zero.

Adding or subtracting fractions

Requires finding a common denominator.

Dividing by a fraction

Requires multiplying by the reciprocal (the 2nd fraction flipped).

$$i$$

The imaginary unit, equivalent to $\sqrt{-1}$.

$$i^2$$

Equivalent to $-1$.