College Algebra & Trigonometry, 2018a

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2.1. REPRESENTING INTERVALS 91 13) −5 −3 −1 4 14) −2 5 7
92 CHAPTER 2. POLYNOMIAL AND RATIONAL FUNCTIONS 2.2 Solution by Graphing In previous courses the solution of linear equations is covered, generally by separating the variables and constants on opposite sides of the equation to isolate the variable. In the previous chapter we examined the solution of quadratic equations, in which the variable is isolated using the technique of completing the square. The major difference between these methods of solution is that, in the solving of quadratic equations, we must contend with several different powers of the variable which makes it considerably more difficult to isolate the variable. There are formulas like the quadratic formula available to solve cubic (x 3 ) and quartic (x 4 ) equations, however these formulas are somewhat cumbersome and archaic. The primary method for solving eqautions of degree higher than 2 is solution by graphing or by algorithm. Solution by algorithm is a very interesting process as there are many different algorithms available. Which algorithm is most appropriate often depends on the types of equations being solved and the technology available to solve them. Two major types of algorithms that rely on the graphincal representation of an equation are called “Double False Position” and “The Newton-Raphson Method.” Many commonly available pieces of techonolgy use one of these methods. Since we have graphing calculators available to us, we will focus on solution by graphing. Whether using a TI (Texas Instruments) or Casio graphing calculator, or a software based graphing ustility such as Graph or Desmos, the solution of these equations focuses on finding the x-intercepts of the graph since this is where the y value is 0. The specific processes for solving equations using each of these different tools will be covered in class. Example Solve for x. x 3 − 3x 2 =2x − 7 The first step is to move all terms to one side of the equation and set them equal to zero. x 3 − 3x 2 − 2x +7=0
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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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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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236 CHAPTER 4. FUNCTIONS 4.9 Optimi
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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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322 CHAPTER 7. COMBINATORICS SET II
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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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