Factor(s),
Factorial notation, 721–722
Factoring, solving nonquadratic equations by, 131–132
Factoring polynomials, 41–49. See also Factoring trinomials
difference and sum of cubes, 45–46
difference of squares, 44–45
Factorization Theorem for Polynomials and, 377, 379
formulas for, 43
greatest common monomial factor and, 41, 42
by grouping, 46–47
over the integers, 41–42
solving quadratic equations by, 106–108
Factoring trinomials
of the form x2+Bx+C, 43
perfect-square trinomials, 44
Factorization Theorem for Polynomials, 377
for polynomials with real coefficients, 379
Factor Theorem, 358–360, 376
Falling objects, distance traveled by, 729, 734–735
False positive in drug testing, 50, 51
Feasible solutions, sets of, 571
Federal taxes, 384
Femur, inferring height from, 205
Fiber-optic cables, cost of, 226–227
Fibonacci (Leonardo of Pisa), 720
Fibonacci sequence, 719–721
Finance. See Investments
Finite sequences, 716
Fiore, Antonio Maria, 376
First component, of ordered pairs, 175
First-degree equations. See Linear equations in one variable
Fixed cost, 227
Focal diameter, of a parabola, 664–666
Focus(i)
of an ellipse, 678
of a hyperbola, 692
of a parabola, 662
FOIL method, 35, 47
Force, gravitational, 403, 408–409
Formulas
change-of-base, 467–468
compound interest, 432, 434–436, 454–455
for converting temperatures between Celsius and Fahrenheit, 87–88
defined, 86
distance, 178–180
factoring, 43
geometry, 88
midpoint, 180–181
quadratic, 111–112
recursive, 719–721
Fractions, 13
adding and subtracting, 14
complex, 56–57
multiplying and dividing, 14
partial, 540. See also Partial-fraction decomposition
properties of, 13
Fraud, detection of, 444
Free-falling objects, 30, 32
Frequency, pitch and, 495–496
Friction and tap-water flow, 61, 63–64
Function(s), 215–234
absolute value, 255, 257
average rate of change of, 241–244
building, 225–227
combining, 281–284
composite. See Composite functions
constant, 235–237, 249, 257
cost, linear, 227
cube root, 251–252, 258
cubing, 240–241, 257
decreasing, 235–237
defined, 216
defined by equations, 218–219
defined by ordered pairs, 217
defined by tables and graphs, 218
difference of, 282
domain of, 220–221
in economics, 227–228
evaluating, 219–220, 224
even-odd, 239–241
exponential. See Exponential functions
graphing, 222–225, 239–241. See also Transformations of functions
greatest integer, 256, 258
identity, 249, 257
increasing, decreasing, and constant, 235–237
inverse. See Inverse functions
linear, 249–251
logarithmic. See Logarithmic functions
objective, 571
one-to-one. See One-to-one functions
piecewise, 252–256
polynomial. See Polynomial functions
power, 334–335
price-demand, linear, 227
price-supply, 227
product of, 282
profit function, 227
properties of, 235–248
quadratic. See Quadratic functions
quotient of, 282
range of, 221
rational. See Rational functions
rational power, 258
reciprocal, 258
reciprocal square, 258
relative maximum and minimum values of, 237–239
representations of, 217–220
square root, 251, 257
squaring, 239–240, 257
step, 256
sum of, 282
transcendental, 436
transformations of. See Transformations of functions
Function notation, 216–217
Fundamental counting principle, 767–769
Fundamental rectangle of a hyperbola, 697
Fundamental Theorem of Algebra, 377
Future value, 432–433