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Polynomials : Asymptotes, Synthetic Division and Even and Odd Power (x-c) Theorem

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1. FIND ALL VERTICAL ASYMPTOTES OF THE FUNCTION.
*******X+5
F (x) -------------------
****4x squared+7

2. WHICH SHOWS THE TRUE STATEMENT FOR THE GRAPH OF THE RATIONAL FUNCTION g.
*******X+2
g(x) -------------------
****x squared+2x-3

3.USE SYNTHETIC DIVISION TO FIND UPPER AND LOWER BOUNDS OF THE REAL ZEROS OF f. f(x) = x fifth + x fourth -5x cubic -3x squared +3x -3
ANSWER: UPPER:__________ LOWER:_________
4. USE THE EVEN AND ODD POWER OF (X-C) THEOREM TO DETERMINE WHERE THE GRAPH OF THE GIVEN POLYNOMIAL WILL CROSS THE X-AXIS AND WHERE THE GRAPH WILL INTERSECT BUT NOT CROSS THE X-AXIS.
Y=(x+7)(x+5)(x-3)squared(x-8)

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Solution Summary

Polynomial problems involving Asymptotes, Synthetic Division and Even and Odd Power (x-c) Theorem are solved. The solution is explained and contains a diagram.

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polynomials/rational functions
________________________________________
1. FIND ALL VERTICAL ASYMPTOTES OF THE FUNCTION.
*******X+5
F (x) -------------------
****4x squared+7

Since , and we know that , we conclude that NO VERTICAL ASYMPTOTES OF THE FUNCTION exist.

2. WHICH SHOWS THE TRUE STATEMENT FOR THE GRAPH OF THE RATIONAL FUNCTION g.
*******X+2
g(x) -------------------
****x ...

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  • BSc , Wuhan Univ. China
  • MA, Shandong Univ.
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  • "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
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