389
Index
389
Absolute Value Functions, 104
Graphing, 105
Solving, 106
Solving Inequalities, 107
Ambiguous Case, 340
Amplitude, 261, 265
Angle, 223
Coterminal Angles, 224
Degree, 223
Radian, 226
Reference Angles, 240
Standard Position, 223
Angular Velocity, 231
Annual Percentage Rate (APR), 162
Annual Percentage Yield (APY), 164
Arclength, 225
Arcsine, Arccosine and Arctangent, 278
Area of a Sector, 230
Average Rate of Change, 23
Change of Base, 180, 185
Circles, 218, 351
Area of a Sector, 230
Equation of a Circle, 218
Points on a Circle, 219, 235
Polar Coordinates, 351
Coefficients, 114
Cofunction Identities, 253
Common Log, 178
Complex Conjugate, 360
Complex Number, 358
Complex Plane, 359
Component Form, 370
Composition of Functions, 35
Formulas, 37
Tables and Graphs, 36
Compound Interest, 162
Concavity, 30
Continuous Growth, 165
Correlation Coefficient, 101, 102
Cosecant, 244
Cosecant Function
Domain, 273
Range, 273
Cosine, 234, 251, 260
Cotangent, 244
Cotangent Function
Domain, 274
Period, 274
Range, 274
Coterminal Angles, 224
Damped Harmonic Motion, 332
Decreasing, 27
Degree, 114, 223
Difference of Logs Property, 185
Domain, 13
Double Angle Identities, 320
Double Zero, 129
Doubling Time, 201
Euler’s Formula, 362
Even Functions, 53
Exponential Functions, 155
Finding Equations, 159
Fitting Exponential Functions to Data, 214
Graphs of Exponential Functions, 168
Solving Exponential Equations, 181
Transformations of Exponential Graphs, 171
Exponential Growth or Decay Function, 156
Exponential Property, 185
Extrapolation, 99
Extrema, 27, 133
Function, 1
Absolute Value Functions, 104
Composition of Functions, 35
Domain and Range, 13
Exponential Functions, 155
Formulas as Functions, 7
Function Notation, 3
Graphs as Functions, 5
Horizontal Line Test, 7
Inverse of a Function, 64
Linear Functions, 71, 73
Logarithmic Functions, 176
One-to-One Function, 2
Parametric Functions, 377
Periodic Functions, 257
Piecewise Function, 20
Polar Functions, 351
Power Functions, 111
Quadratic Functions, 118
Radical Functions, 149, 150
Rational Functions, 136, 139
Sinusoidal Functions, 259
Solving & Evaluating, 5
Tables as Functions, 3
Tangent Function, 270
Vertical Line Test, 6
Half-Angle Identities, 327
Half-Life, 198
Hole, 141
Horizontal Asymptote, 138, 142
Horizontal Intercept, 84
Horizontal Line Test, 7
Horizontal Lines, 85
Imaginary Number, 358
Complex Conjugate, 360
Complex Number, 358
Complex Plane, 359
Euler’s Formula, 362
Polar Form of Complex Numbers, 361, 362
Increasing, 27
Inflection Point, 30
Intercepts, 123, 127, 128, 132, 143
Graphical Behavior, 128
Writing Equations, 132
Interpolation, 99
Intersections of Lines, 87
Interval Notation, 15
Union, 15
Inverse of a Function, 64
Properties of Inverses, 68
Inverse Properties, 185
Inversely Proportional, 136
Inversely Proportional to the Square, 136
Inverses, 149
Law of Cosines
General Pythagorean Theorem, 343
Law of Sines
Ambiguous Case, 340
Leading Coefficient, 114
Leading Term, 114
Least-Square Regression, 100
Limaçons, 352
Linear Functions, 71, 73
Fitting Linear Models to Data, 98
Graphing, 79
Horizontal Intercept, 84
Horizontal Lines, 85
Intersections of Lines, 87
Least-Square Regression, 100
Modeling, 90
Parallel Lines, 85
Perpendicular Lines, 86
Veritcal Lines, 85
Vertical Intercept, 80
Linear Velocity, 231
Lissajous Figure, 380
Local Maximum, 27
Local Minimum, 27
Logarithmic Functions, 176
Change of Base, 180, 185
Common Log, 178
Difference of Logs Property, 185
Exponential Property, 179, 185
Graphs of Logarithmic Functions, 192
Inverse Properties, 176, 185
Logarithmic Scales, 204
Log-Log Graph, 212
Moment Magnitude Scale, 207
Natural Log, 178
Orders of Magnitude, 207
Semi-Log Graph, 212
Sum of Logs Property, 185
The Logarithm, 176
Transformations of the Logarithmic Function, 194
Log-Log Graph, 212
Long Run Behavior, 112, 115, 137
Mathematical Modeling, 71
Midline, 262, 265
Model Breakdown, 100
Moment Magnitude Scale, 207
Natural Log, 178
Negative Angle Identities, 302
Newton's Law of Cooling, 203
Nominal Rate, 162
Odd Functions, 53
One-to-One Function, 2, 7
Orders of Magnitude, 207
Parallel Lines, 85
Parametric Functions, 377
Converting from Parametric to Cartesian, 380
Lissajous Figure, 380
Parameterizing Curves, 382
Period, 257, 265
Periodic Functions, 257
Period, 257
Sinusoidal, 259
Perpendicular Lines, 86
Phase Shift, 268
Piecewise Function, 20
Polar Coordinates
Converting Points, 349
Polar Functions, 351
Converting To and From Cartesian Coordinates, 354
Euler’s Formula, 362
Limaçons, 352
Polar Form of Complex Numbers, 361, 362
Roses, 352, 353
Polynomial, 114
Coefficients, 114
Degree, 114
Horizontal Intercept, 129, 132
Leading Coefficient, 114
Leading Term, 114
Solving Inequalities, 130
Term, 114
Power Functions, 111
Characterisitcs, 112
Power Reduction Identities, 327
Product to Sum Identities, 314
Pythagorean Identity, 236, 248
Alternative Forms, 248, 302
Pythagorean Theorem, 217
Quadratic Formula, 125
Quadratic Functions, 118
Quadratic Formula, 125
Standard Form, 120, 121
Transformation Form, 120
Vertex Form, 120
Radian, 226
Radical Functions, 149, 150
Range, 13
Rate of Change, 23
Average, 23
Using Function Notation, 25
Rational Functions, 136, 139
Hole, 141
Intercepts, 143
Long Run Behavior, 141
Reciprocal Identities, 302
Reference Angles, 240
Roses, 352, 353
Secant, 244
Secant Function
Domain, 273
Range, 273
Semi-Log Graph, 212
Set-Builder Notation, 15
Short Run Behavior, 115, 118, 123, 127, 137
Sine, 234, 251, 260
Single Zero, 129
Sinusoidal Functions, 259
Amplitude, 261, 265
Damped Harmonic Motion, 332
Midline, 262, 265
Modeling, 295
Period, 257, 265
Phase Shift, 268
Solving Trig Equations, 290
Slope, 73, 74, 80
Decreasing, 73
Increasing, 73
Standard Form, 120, 121
Standard Position, 223
Sum and Difference Identities, 308
Sum of Logs Property, 185
Sum to Product Identities, 315
Tangent, 244, 251
Tangent Function, 270
Domain, 270
Period, 270
Range, 270
Term, 114
The Logarithm, 176
Toolkit Functions, 11
Domains and Ranges of Toolkit Functions, 18
Transformation Form, 120
Transformations of Functions, 43
Combining Horizontal Transformations, 59
Combining Vertical Transformations, 58
Horizontal Reflections, 50
Horizontal Shifts, 46
Horizontal Stretch or Compression, 56
Vertical Reflections, 50
Vertical Shifts, 44
Vertical Stretch or Compression, 54
Trigonometric Identities, 245
Alternative Forms of the Pythagorean Identity, 248, 302
Cofunction Identities, 253
Double Angle Identities, 320
Half-Angle Identities, 327
Negative Angle Identities, 302
Power Reduction Identities, 327
Product to Sum Identities, 314
Pythagorean Identity, 236
Reciprocal Identities, 302
Sum and Difference Identities, 308
Sum to Product Identities, 315
Trigonometry
Cosecant, 244
Cosine, 234, 251, 260
Cotangent, 244
Right Triangles, 251
Secant, 244
Sine, 234, 251, 260
SohCahToa, 251
Solving Trig Equations, 290
Tangent, 244, 251
The Pythagorean Theorem, 217
Unit Circle, 241
Triple Zero, 129
Unit Circle, 241
Vector, 367, 370
Adding Vectors Geometrically, 368
Adding, Subtracting, or Scaling Vectors in Component Form, 372
Geometrically Scaling a Vector, 369
Vertex, 118, 120
Vertex Form, 120
Vertical Asymptote, 137, 140
Vertical Intercept, 80
Vertical Line Test, 6
Vertical Lines, 85
389