Polynomial and Rational Functions Flashcards

Grade 11 · Math · Flashcards

Key terms, theorems, and rules for analyzing polynomial and rational functions.

Flashcards

Fundamental Theorem of Algebra: Every polynomial of degree n has exactly n complex zeros (counting multiplicity)
Rational Root Theorem: Possible rational zeros = ±(factors of constant term) / (factors of leading coefficient)
Even multiplicity zero: Graph touches (bounces off) x-axis; does not cross
Odd multiplicity zero: Graph crosses x-axis at that zero
Vertical asymptote: x = a where denominator = 0 and numerator ≠ 0
Hole (removable discontinuity): Occurs when a common factor cancels from numerator and denominator
Horizontal asymptote: deg(p) < deg(q): y = 0
Horizontal asymptote: deg(p) = deg(q): y = (leading coeff of p) / (leading coeff of q)
Oblique asymptote: Occurs when deg(numerator) = deg(denominator) + 1; found by polynomial long division
End behavior (even degree, positive leading): Both ends → +∞
End behavior (odd degree, positive leading): Left end → -∞, right end → +∞
Complex conjugate pairs: Non-real zeros of polynomials with real coefficients always come in conjugate pairs a ± bi
Synthetic division: Shortcut for dividing polynomial by (x - c) and evaluating f(c)