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Numbers and Their Disguises |
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Multiplying and dividing fractions, adding and subtracting fractions, parentheses, exponents, roots, percent, scientific notation, calculators, rounding, intervals |
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1 | (24) |
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Completing the square in one and two variables |
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25 | (5) |
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Equations of degree 1 and 2, solving other types of equations, rational equations, the zero-factor property |
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30 | (17) |
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Algebraic Functions and Graphs |
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Functions and Their Graphs |
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Introduction, equations of lines, power functions, shifting graphs, intersection of curves |
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47 | (28) |
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Cyclic Phenomena: The Six Basic Trigonometric Functions |
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Angles, definitions of the six trigonometric functions, basic identities, special angles, sum formulas |
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75 | (20) |
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The family of exponential functions, the function ex |
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95 | (6) |
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Composition and Inverse Functions |
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Composite functions, the idea of inverses, finding an inverse of f given by a graph, finding the inverse of f given by an expression |
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101 | (12) |
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Definition of logarithms, logarithms as inverses of exponential functions, laws of logarithms, the natural logarithm |
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113 | (13) |
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Inverse Trigonometric Functions |
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The definition of arcsin x, the functions arctan x and arcsec x, inverse trigonometric identities |
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126 | (13) |
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Changing the Form of a Function |
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Factoring, canceling, long division, rationalizing, extracting a factor from under a root |
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139 | (14) |
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Simplifying Algebraic Expressions |
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Working with difference quotients and rational functions, canceling common factors, rationalizing expressions |
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153 | (7) |
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Decomposition of Functions |
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Inner, outer, and outermost functions, decomposing composite functions |
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160 | (2) |
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Equations of Degree 1 Revisited |
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Solving linear equations involving derivatives |
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162 | (4) |
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Related Rates, Applied Max-Min Problems |
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Word Problems, Algebraic and Transcendental |
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Algebraic word problems, the geometry of rectangles, circles and spheres, trigonometric word problems, right angle triangles, the law of sines and the law of cosines, exponential growth and decay |
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166 | (12) |
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Integrating Trigonometric Functions |
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Rewriting trigonometric expressions using identities |
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178 | (5) |
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Appendices (Use as needed) |
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183 | (3) |
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Derivation of the Quadratic Formula |
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186 | (3) |
Answers to Odd-Numbered Exercises |
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189 | (22) |
Index |
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211 | |