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.
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- What is the degree of a polynomial function?
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The highest exponent among its terms- What determines a polynomial's end behavior?
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Its degree and leading coefficient- What is a zero (root) of a polynomial?
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A value where the function equals zero- What is multiplicity of a zero?
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How many times a factor repeats in the polynomial- What does an even multiplicity zero do at the x-axis?
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The graph touches and turns back, without crossing- What does an odd multiplicity zero do at the x-axis?
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The graph crosses through- What is the Fundamental Theorem of Algebra?
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A degree n polynomial has exactly n complex roots, counted with multiplicity- What is synthetic division used for?
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Dividing a polynomial by a linear factor efficiently- What is the Remainder Theorem?
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Dividing f(x) by (x - a) gives a remainder equal to f(a)- What is the Rational Root Theorem used to find?
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Possible rational zeros of a polynomial- What are complex conjugate roots?
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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?
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Values that make the denominator zero, after simplifying- What is a rational function's horizontal asymptote determined by?
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Comparing the degrees of the numerator and denominator- What is a slant (oblique) asymptote?
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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?
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A point excluded due to a factor that cancels between numerator and denominator
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