College Algebra & Trigonometry, 2018a

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2.3. SOLUTION OF POLYNOMIAL INEQUALITIES BY GRAPHING 97 10 y ≥ 0 5 A B y ≥ 0 −3 −2 −1 C 1 −5 The indicated roots of the function (A, B and C) are the x-values that make y equal to zero. These points divide the graph between the regions where y is greater than zero and the regions where y is less than zero. The solution to the given inequlaity 2x 3 +8x 2 +5x − 3 ≥ 0 are A≤ x ≤B ORx ≥C. When we find the values of A, B and C: A= −3,B≈−1.366 and C≈ 0.366, we can complete the solution to the problem. 2x 3 +8x 2 +5x − 3 ≥ 0 −3 ≤ x ≤−1.366 OR x ≥ 0.366 Example Solve the given inequality. x 4 − 2x 3 − 5x 2 +8x +3≤ 0 First, we graph the function:
98 CHAPTER 2. POLYNOMIAL AND RATIONAL FUNCTIONS 5 −2 −1 1 2 y = x 4 − 2x 3 − 5x 2 +8x +3 −5 In this problem, we’re looking for the intervals of x values that make y less than or equal to zero. First, we identify the roots of the function: 5 x ≈−2.034 x ≈ 1.806 −3 −2 −1 1 2 3 x ≈−0.320 x ≈ 2.549 −5 Next, we’ll identify the intervals where the y values are less than zero:
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College Algebra & Trigonometry
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c○2018 Richard W. Beveridge This
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4 CONTENTS 2.4 Solution of Rational
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6 CONTENTS 8.2 The Trigonometric Ra
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8 CONTENTS
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10 CHAPTER 1. ALGEBRA REVIEW Exampl
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12 CHAPTER 1. ALGEBRA REVIEW 2(x +3
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14 CHAPTER 1. ALGEBRA REVIEW 1.2 Fa
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16 CHAPTER 1. ALGEBRA REVIEW Trinom
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18 CHAPTER 1. ALGEBRA REVIEW Here,
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20 CHAPTER 1. ALGEBRA REVIEW (3x ?)
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22 CHAPTER 1. ALGEBRA REVIEW which
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24 CHAPTER 1. ALGEBRA REVIEW Differ
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30 CHAPTER 1. ALGEBRA REVIEW Then,
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32 CHAPTER 1. ALGEBRA REVIEW We can
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34 CHAPTER 1. ALGEBRA REVIEW PROGRA
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40 CHAPTER 1. ALGEBRA REVIEW devise
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42 CHAPTER 1. ALGEBRA REVIEW −7i(
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148 CHAPTER 3. EXPONENTS AND LOGARI
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190 CHAPTER 4. FUNCTIONS by substit
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192 CHAPTER 4. FUNCTIONS 4.2 Domain
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194 CHAPTER 4. FUNCTIONS Exercises
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196 CHAPTER 4. FUNCTIONS 8) 12 10 8
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198 CHAPTER 4. FUNCTIONS We can use
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200 CHAPTER 4. FUNCTIONS 3) 20 16 1
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202 CHAPTER 4. FUNCTIONS Vertical S
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204 CHAPTER 4. FUNCTIONS Now, if, i
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206 CHAPTER 4. FUNCTIONS So the gra
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208 CHAPTER 4. FUNCTIONS Stretching
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210 CHAPTER 4. FUNCTIONS Multiplyin
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214 CHAPTER 4. FUNCTIONS 3) Match e
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216 CHAPTER 4. FUNCTIONS 6) f(x) 7)
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218 CHAPTER 4. FUNCTIONS Being fami
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222 CHAPTER 4. FUNCTIONS 4.6 Piecew
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226 CHAPTER 4. FUNCTIONS 4.7 Compos
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228 CHAPTER 4. FUNCTIONS 17) h(x) =
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230 CHAPTER 4. FUNCTIONS Original f
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232 CHAPTER 4. FUNCTIONS Then we sw
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234 CHAPTER 4. FUNCTIONS 19) f(x) =
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238 CHAPTER 4. FUNCTIONS 2) The gra
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242 CHAPTER 4. FUNCTIONS 8) A recta
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244 CHAPTER 4. FUNCTIONS So, our fi
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248 CHAPTER 4. FUNCTIONS Distance O
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250 CHAPTER 4. FUNCTIONS The graph
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252 CHAPTER 4. FUNCTIONS Distance/T
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254 CHAPTER 4. FUNCTIONS The graph
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256 CHAPTER 4. FUNCTIONS 3) A power
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258 CHAPTER 5. CONIC SECTIONS - CIR
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288 CHAPTER 6. SEQUENCES AND SERIES
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306 CHAPTER 7. COMBINATORICS differ
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308 CHAPTER 7. COMBINATORICS Exampl
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344 CHAPTER 8. RIGHT TRIANGLE TRIGO
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438 CHAPTER 10. TRIGONOMETRIC IDENT
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472 CHAPTER 11. THE LAW OF SINES TH
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College Algebra & Trigonometry, 2018a

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