 1.1: Give an example of each of the following:(a) A natural number(b) An...
 1.2: Complete each statement and name the property of realnumbers you ha...
 1.3: . Express the set of real numbers between but not including 2and 7 ...
 1.4: The symbol 0 x 0 stands for the of the number x.If x is not 0, then...
 1.5: The distance between a and b on the real line is d 1a, b2 . So the ...
 1.6: 6. (a) Is the sum of two rational numbers always a rationalnumber?(...
 1.7: (a) Is a b equal to b a?(b) Is 21a 52 equal to 2a 10?
 1.8: . (a) Is the distance between any two different real numbersalways ...
 1.9: Real Numbers List the elements of the given set that are(a) natural...
 1.10: Real Numbers List the elements of the given set that are(a) natural...
 1.11: Properties of Real Numbers State the property of realnumbers being ...
 1.12: Properties of Real Numbers State the property of realnumbers being ...
 1.13: Properties of Real Numbers State the property of realnumbers being ...
 1.14: Properties of Real Numbers State the property of realnumbers being ...
 1.15: Properties of Real Numbers State the property of realnumbers being ...
 1.16: Properties of Real Numbers State the property of realnumbers being ...
 1.17: Properties of Real Numbers State the property of realnumbers being ...
 1.18: Properties of Real Numbers State the property of realnumbers being ...
 1.19: Properties of Real Numbers Rewrite the expressionusing the given pr...
 1.20: Properties of Real Numbers Rewrite the expressionusing the given pr...
 1.21: Properties of Real Numbers Rewrite the expressionusing the given pr...
 1.22: Properties of Real Numbers Rewrite the expressionusing the given pr...
 1.23: Properties of Real Numbers Use properties of realnumbers to write t...
 1.24: Properties of Real Numbers Use properties of realnumbers to write t...
 1.25: Properties of Real Numbers Use properties of realnumbers to write t...
 1.26: Properties of Real Numbers Use properties of realnumbers to write t...
 1.27: Properties of Real Numbers Use properties of realnumbers to write t...
 1.28: Properties of Real Numbers Use properties of realnumbers to write t...
 1.29: Arithmetic Operations Perform the indicatedoperations. (a) 310 415 ...
 1.30: Arithmetic Operations Perform the indicatedoperations. (a) 23 35 (b...
 1.31: Arithmetic Operations Perform the indicatedoperations. . (a) 23A6 3...
 1.32: Arithmetic Operations Perform the indicatedoperations. (a)223232 (b...
 1.33: Inequalities Place the correct symbol (, , or ) inthe space. a) 3 7...
 1.34: Inequalities Place the correct symbol (, , or ) in the space.(a) 23...
 1.35: Inequalities State whether each inequality is true orfalse. (a) 3 4...
 1.36: Inequalities State whether each inequality is true orfalse. (a) !3 ...
 1.37: Inequalities State whether each inequality is true orfalse. (a) 102...
 1.38: Inequalities State whether each inequality is true orfalse. (a) 711...
 1.39: Inequalities Write each statement in terms ofinequalities. (a) x is...
 1.40: Inequalities Write each statement in terms ofinequalities. (a) y is...
 1.41: Sets Find the indicated set ifA 51, 2, 3, 4, 5, 6, 76 B 52, 4, 6, 8...
 1.42: Sets Find the indicated set ifA 51, 2, 3, 4, 5, 6, 76 B 52, 4, 6, 8...
 1.43: Sets Find the indicated set ifA 51, 2, 3, 4, 5, 6, 76 B 52, 4, 6, 8...
 1.44: Sets Find the indicated set ifA 51, 2, 3, 4, 5, 6, 76 B 52, 4, 6, 8...
 1.45: Sets Find the indicated set ifA 5x 0 x 26 B 5x 0 x 46C 5x 0 1 x 56(...
 1.46: Sets Find the indicated set ifA 5x 0 x 26 B 5x 0 x 46C 5x 0 1 x 56 ...
 1.47: Intervals Express the interval in terms of inequalities,and then gr...
 1.48: Intervals Express the interval in terms of inequalities,and then gr...
 1.49: Intervals Express the interval in terms of inequalities,and then gr...
 1.50: Intervals Express the interval in terms of inequalities,and then gr...
 1.51: Intervals Express the interval in terms of inequalities,and then gr...
 1.52: Intervals Express the interval in terms of inequalities,and then gr...
 1.53: Intervals Express the inequality in interval notation,and then grap...
 1.54: Intervals Express the inequality in interval notation,and then grap...
 1.55: Intervals Express the inequality in interval notation,and then grap...
 1.56: Intervals Express the inequality in interval notation,and then grap...
 1.57: Intervals Express the inequality in interval notation,and then grap...
 1.58: Intervals Express the inequality in interval notation,and then grap...
 1.59: Intervals Express each set in interval notation.
 1.60: Intervals Express each set in interval notation.
 1.61: Intervals Graph the set.12, 02 11, 12
 1.62: Intervals Graph the set. 12, 02 11, 12
 1.63: Intervals Graph the set. 34, 64 30, 82
 1.64: Intervals Graph the set.34, 62 30, 82
 1.65: Intervals Graph the set.. 1`, 42 14, `2
 1.66: Intervals Graph the set.1`, 64 12, 102
 1.67: Absolute Value Evaluate each expression (a) 0 100 0
 1.68: Absolute Value Evaluate each expression a) 0 100 0 (b) 0 73 0
 1.69: Absolute Value Evaluate each expression (a) 0 !5 5 0 (b) 0 10 p 0
 1.70: Absolute Value Evaluate each expression(a) @ 0 6 0 0 4 0 @ (b) 10 1 0
 1.71: Absolute Value Evaluate each expression (a) 0 122 # 6 0 (b) 0 A13B ...
 1.72: Absolute Value Evaluate each expression(a) `624 ` (b) `7 1212 7 `
 1.73: Find the distance between the givennumbers.
 1.74: Find the distance between the givennumbers.
 1.75: Find the distance between the givennumbers.
 1.76: Find the distance between the givennumbers.
 1.77: Repeating Decimal Express each repeating decimal asa fraction. (See...
 1.78: Repeating Decimal Express each repeating decimal asa fraction. (See...
 1.79: Simplifying Absolute Value Express the quantity withoutusing absolu...
 1.80: Simplifying Absolute Value Express the quantity withoutusing absolu...
 1.81: Simplifying Absolute Value Express the quantity withoutusing absolu...
 1.82: Simplifying Absolute Value Express the quantity withoutusing absolu...
 1.83: Signs of Numbers Let a, b, and c be real numberssuch that a 0, b 0,...
 1.84: Signs of Numbers Let a, b, and c be real numberssuch that a 0, b 0,...
 1.85: Area of a Garden Marys backyard vegetable garden measures20 ft by 3...
 1.86: Temperature Variation The bar graph shows the daily hightemperature...
 1.87: Mailing a Package The post office will accept onlypackages for whic...
 1.88: DISCUSS: Sums and Products of Rational and IrrationalNumbers Explai...
 1.89: 9. DISCOVER PROVE: Combining Rational and IrrationalNumbers Is 12 !...
 1.90: . DISCOVER: Limiting Behavior of Reciprocals Complete thetables. Wh...
 1.91: Discover: Locating Irrational Numbers on the Real LineUsing the fig...
 1.92: 2. Prove: Maximum and Minimum Formulas Let max1a, b2denote the maxi...
 1.93: . Write: Real Numbers in the Real World Write a paragraphdescribing...
 1.94: . Discuss: Commutative and Noncommutative OperationsWe have learned...
 1.95: PROVE: Triangle Inequality We prove Property 5 of absolutevalues, t...
 1.96: Comparing Roots Without using a calculator, determinewhich number i...
 1.97: Distance to the Nearest Star Proxima Centauri, the starnearest to o...
 1.98: Speed of Light The speed of light is about 186,000 mi/s.Use the inf...
 1.99: Volume of the Oceans The average ocean depth is3.7 103 m, and the a...
 1.100: National Debt As of July 2013, the population of theUnited States w...
 1.101: Number of Molecules A sealed room in a hospital, measuring5 m wide,...
 1.102: Number of Molecules A sealed room in a hospital, measuring5 m wide,...
 1.103: Speed of a Skidding Car Police use the formulas "30fd to estimate t...
 1.104: Distance from the Earth to the Sun It follows fromKeplers Third Law...
 1.105: Discuss:How Big is a Billion? If you had a million (106)dollars in ...
 1.106: Discuss: Easy Powers that Look Hard Calculate theseexpressions in y...
 1.107: 7. DISCOVER: Limiting Behavior of Powers Complete the followingtabl...
 1.108: PROVE: Laws of Exponents Prove the following Laws ofExponents for t...
 1.109: PROVE: Laws of Exponents Prove the following Laws ofExponents.(a) L...
 1.110: Factoring Completely Factor the expression completely. r2 6rs 9s2
 1.111: Factoring Completely Factor the expression completely. . 1a b22 1a b22
 1.112: Factoring Completely Factor the expression completely. 1 1xb2 a 1 1xb2
 1.113: Factoring Completely Factor the expression completely. x21x2 12 91x...
 1.114: Factoring Completely Factor the expression completely. 1a2 12b2 41a...
 1.115: Factoring Completely Factor the expression completely. 8x3 125
 1.116: Factoring Completely Factor the expression completely. x6 64
 1.117: Factoring Completely Factor the expression completely. x3 2x2 x
 1.118: Factoring Completely Factor the expression completely. 3x3 27x
 1.119: Factoring Completely Factor the expression completely. x4y3 x2y5
 1.120: Factoring Completely Factor the expression completely. 18y3x2 2xy4
 1.121: Factoring Completely Factor the expression completely. 3x3 x2 12x 4
 1.122: Factoring Completely Factor the expression completely. 9x3 18x2 x 2
 1.123: Factoring Completely Factor the expression completely. 1x 12 1x 222...
 1.124: Factoring Completely Factor the expression completely. y41y 223 y51...
 1.125: Factoring Completely Factor the expression completely. 1a2 122 71a2...
 1.126: Factoring Completely Factor the expression completely. 1a2 2a22 21a...
 1.127: Factoring Completely Factor the expression completely.(This type of...
 1.128: Factoring Completely Factor the expression completely.(This type of...
 1.129: Factoring Completely Factor the expression completely.(This type of...
 1.130: Verifying Identities Show that the following identitieshold.
 1.131: Verifying Identities Show that the following identitieshold. (a) ab...
 1.132: Verifying Identities Show that the following identitieshold. 1a2 b2...
 1.133: Factoring Completely Factor the following expressioncompletely: 4a2...
 1.134: Factoring x 4 ax 2 b A trinomial of the formx 4 ax 2 b can sometime...
 1.135: Volume of Concrete A culvert is constructed out of largecylindrical...
 1.136: Mowing a Field Asquare field in a certainstate park is mowedaround ...
 1.137: DISCOVER:Degree of a Sum or Product of PolynomialsMake up several p...
 1.138: DISCUSS: The Power of Algebraic Formulas Use the Differenceof Squar...
 1.139: 9. DISCUSS: The Power of Algebraic Formulas Use theSpecial Product ...
 1.140: DISCOVER:Differences of Even Powers(a) Factor the expressions compl...
 1.141: DISCOVER: Factoring An 1(a) Verify the following formulas by expand...
 1.142: .PROVE: Special Factoring Formulas Prove the followingformulas by e...
 1.143: Inequalities Solve the inequality graphically. 4x 3 x 2
 1.144: Inequalities Solve the inequality graphically. x 3 4x 2 5x 2
 1.145: Inequalities Solve the inequality graphically. x 4 4x 2 12 x 1
 1.146: Inequalities Solve the inequality graphically. x 2 16 0 10 0
 1.147: Circles and Lines Find equations for the circle andthe line in the ...
 1.148: Circles and Lines Find equations for the circle andthe line in the ...
 1.149: Variation Suppose that M varies directly as z, andM 120 when z 15. ...
 1.150: Variation Suppose that z is inversely proportional to y, andthat z ...
 1.151: Light Intensity The intensity of illumination I from a lightvaries ...
 1.152: Vibrating String The frequency of a vibrating string underconstant ...
 1.153: Terminal Velocity The terminal velocity of a parachutist isdirectly...
 1.154: Range of a Projectile The maximum range of a projectileis directly ...
Solutions for Chapter 1: Fundamentals
Full solutions for Precalculus: Mathematics for Calculus (Standalone Book)  7th Edition
ISBN: 9781305071759
Solutions for Chapter 1: Fundamentals
Get Full SolutionsChapter 1: Fundamentals includes 154 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions. Since 154 problems in chapter 1: Fundamentals have been answered, more than 5137 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Precalculus: Mathematics for Calculus (Standalone Book), edition: 7. Precalculus: Mathematics for Calculus (Standalone Book) was written by and is associated to the ISBN: 9781305071759.

Complex plane
A coordinate plane used to represent the complex numbers. The xaxis of the complex plane is called the real axis and the yaxis is the imaginary axis

Cube root
nth root, where n = 3 (see Principal nth root),

First quartile
See Quartile.

Increasing on an interval
A function ƒ is increasing on an interval I if, for any two points in I, a positive change in x results in a positive change in.

Interquartile range
The difference between the third quartile and the first quartile.

Interval
Connected subset of the real number line with at least two points, p. 4.

Law of sines
sin A a = sin B b = sin C c

Limit to growth
See Logistic growth function.

Mathematical induction
A process for proving that a statement is true for all natural numbers n by showing that it is true for n = 1 (the anchor) and that, if it is true for n = k, then it must be true for n = k + 1 (the inductive step)

Obtuse triangle
A triangle in which one angle is greater than 90°.

Onetoone function
A function in which each element of the range corresponds to exactly one element in the domain

Polynomial interpolation
The process of fitting a polynomial of degree n to (n + 1) points.

Power function
A function of the form ƒ(x) = k . x a, where k and a are nonzero constants. k is the constant of variation and a is the power.

Power regression
A procedure for fitting a curve y = a . x b to a set of data.

Powerreducing identity
A trigonometric identity that reduces the power to which the trigonometric functions are raised.

Real number
Any number that can be written as a decimal.

Simple harmonic motion
Motion described by d = a sin wt or d = a cos wt

Standard position (angle)
An angle positioned on a rectangular coordinate system with its vertex at the origin and its initial side on the positive xaxis

Transpose of a matrix
The matrix AT obtained by interchanging the rows and columns of A.

Zero factorial
See n factorial.