Precalculus, Unit 2: Polynomial and Rational Functions. Key terms, formulas, and worked-example cues a high school student meets for this unit, building on prior units. Front: the term, formula name, or short problem cue. Back: the definition, formula, or solution method.
30 cards · basic cards · AI-written, checked twice. Edit anything.
- What is the degree of a polynomial function?
- The highest exponent among its terms
- What determines a polynomial's end behavior?
- Its degree and leading coefficient
- What is a zero (root) of a polynomial?
- A value where the function equals zero
- What is multiplicity of a zero?
- How many times a factor repeats in the polynomial
- What does an even multiplicity zero do at the x-axis?
- The graph touches and turns back, without crossing
- What does an odd multiplicity zero do at the x-axis?
- The graph crosses through
- What is the Fundamental Theorem of Algebra?
- A degree n polynomial has exactly n complex roots, counted with multiplicity
- What is synthetic division used for?
- Dividing a polynomial by a linear factor efficiently
- What is the Remainder Theorem?
- Dividing f(x) by (x - a) gives a remainder equal to f(a)
- What is the Rational Root Theorem used to find?
- Possible rational zeros of a polynomial
- What are complex conjugate roots?
- Pairs of complex roots, a+bi and a-bi, that occur together in real polynomials
- What is a rational function's vertical asymptote determined by?
- Values that make the denominator zero, after simplifying
- What is a rational function's horizontal asymptote determined by?
- Comparing the degrees of the numerator and denominator
- What is a slant (oblique) asymptote?
- A diagonal asymptote occurring when the numerator's degree is one more than the denominator's
- What is a hole in a rational function's graph?
- A point excluded due to a factor that cancels between numerator and denominator
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