AP Precalculus Unit 1 Review

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What is an odd function?

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A function f(x) is considered odd if for every x in the domain, f(-x) = -f(x). This means the graph of the function is symmetric with respect to the origin.

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CCSS.HSF.BF.B.3

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What does it mean if x = a is a zero of a polynomial function p(x)?

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If x = a is a zero of p(x), it means that p(a) = 0. This implies that (x - a) is a linear factor of the polynomial.

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CCSS.HSF-IF.C.7C

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How do you calculate the Average Rate of Change (ROC) between two points on a graph?

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The Average Rate of Change between two points (x1, y1) and (x2, y2) is calculated using the formula: Average ROC = (y2 - y1) / (x2 - x1), which represents the slope of the line connecting the two points.

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CCSS.8.F.B.4

CCSS.HSF.IF.B.6

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What is a root or zero of a polynomial function?

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A root or zero of a polynomial function p(x) is a value a such that p(a) = 0. It indicates where the graph of the polynomial intersects the x-axis.

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CCSS.HSF-IF.C.7C

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If a polynomial function has a degree n, what does that imply about its zeros?

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The degree n of a polynomial function indicates the maximum number of zeros (real or complex) it can have. For example, a polynomial of degree 5 can have up to 5 zeros.

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What is the relationship between the degree of a polynomial and its end behavior?

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The degree of a polynomial determines its end behavior: if the degree is even, the ends of the graph will either both go up or both go down; if the degree is odd, one end will go up and the other will go down.

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What is the significance of complex zeros in polynomial functions?

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Complex zeros occur in conjugate pairs. If a polynomial has real coefficients and a complex zero, its conjugate must also be a zero.

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CCSS.HSN.CN.C.9

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What is the Fundamental Theorem of Algebra?

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The Fundamental Theorem of Algebra states that every non-constant polynomial function of degree n has exactly n roots in the complex number system, counting multiplicities.

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CCSS.HSN.CN.C.9

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How can you determine the number of real zeros of a polynomial function?

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The number of real zeros can be determined using the Descartes' Rule of Signs, which provides a way to estimate the number of positive and negative real zeros based on the sign changes in the polynomial.

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What is the difference between a polynomial function and a rational function?

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A polynomial function is a function that can be expressed in the form p(x) = a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + a_0, where a_n are constants and n is a non-negative integer. A rational function is a ratio of two polynomial functions.