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# MAT 109, Chapter 5 Study Guide MAT 109

Barry University

GPA 3.7

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## Popular in Precalculus Mathematics 1

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This 4 page Study Guide was uploaded by Sterling Notetaker on Wednesday September 7, 2016. The Study Guide belongs to MAT 109 at Barry University taught by Dr. Singh in Fall 2016. Since its upload, it has received 10 views. For similar materials see Precalculus Mathematics 1 in Mathmatics at Barry University.

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Date Created: 09/07/16

MAT 109 Precalculus Mathematics 1 Chapter 5 Study Guide Notes L. Sterling September 9th, 2016 Abstract Provide a generalization to each of the key terms listed in this section. 1 Factor Theorem First o▯, let f be a polynomial function. Since x ▯ c is a factor of f(x) i▯ [if and only if] f(c) be equaled to 0. ▯ If f(c) = 0, then x ▯ c would be a f(x)s factor. ▯ If x ▯ c would be a f(x)s factor, then f(c) = 0. 2 Intermediate Value Theorem This is denoting f to be a polynomial function while if both a < b with f(a) and f(b) being the opposite sign, then theres fs at least one actual [real] zero between for a and b. 1 3 Polynomial Function f (x) = a x + a xn▯1 + ::: + a x + a n n▯1 1 0 an 6= 0 Domain : All Real Numbers At Most [Turning Points] : n ▯ 1 n End Behavior : y = n x for jxj 4 Power Function x 4.1 f (x) = n ; n ▯ 2 Domain : All Real Numbers Range Nonnegative Real Numbers Function : Even Passing Points : (▯1; 1); (0; 0); (1; 1) Increasing : (0; 1) Decreasing : (▯1; 0) 4.2 f (x) = n ; n ▯ 3 Domain : All Real Numbers Range All Real Numbers 2 Function : Odd Passing Points : (▯1; ▯1); (0; 0); (1; 1) Increasing : (▯1; 1) Decreasing : None 5 Rational Function p : Polynomial Functions q : Polynomial Functions q : Not a Zero Polynomial p(x) R(x) = q (x) Domain : fx j q (x) 6 0g 6 Rational Zeros Theorem Since you are letting f is a polynomial function of degree 1 or any higher in the following form that note that each coe▯cient is an integer: n n▯1 f (x) = n x + a n▯1x + ::: +1a x +0a an 6= 0 a0 6= 0 3 p If you haveq[a rational zero of f] in its lowest terms, then you would have p being an a factor0a with q being a factornof a . 7 Real Zero of a Polynomial Function Real Numbers : f (x) = 0 Real Zeros : X ▯ Intercepts 8 Remainder Theorem First o▯, let f be a polynomial function. Since f(x) is the dividend, if f(x) is f(x) being divided by x ▯ c, which would look lx▯c, then the remainder would technically be f(c). 4

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