 1.1.1: Give an example of numbers a and b such that a b.
 1.1.2: Which numbers satisfy a = a? Which satisfy a=a? What about a ...
 1.1.3: Give an example of numbers a and b such that a + b < a+b.
 1.1.4: Are there numbers a and b such that a + b > a+b?
 1.1.5: What are the coordinates of the point lying at the intersection of ...
 1.1.6: In which quadrant do the following points lie? (a) (1, 4) (b) (3, 2...
 1.1.7: What is the radius of the circle with equation (x 7)2 + (y 8)2 = 9?
 1.1.8: The equation f (x) = 5 has a solution if (choose one): (a) 5 belong...
 1.1.9: What kind of symmetry does the graph have if f (x) = f (x)?
 1.1.10: Is there a function that is both even and odd?
 1.1.11: In Exercises 912, write the inequality in the form a 2x + 1 < 5
 1.1.12: In Exercises 912, write the inequality in the form a 3x 4 < 2
 1.1.13: In Exercises 1318, express the set of numbers x satisfying the give...
 1.1.14: In Exercises 1318, express the set of numbers x satisfying the give...
 1.1.15: In Exercises 1318, express the set of numbers x satisfying the give...
 1.1.16: In Exercises 1318, express the set of numbers x satisfying the give...
 1.1.17: In Exercises 1318, express the set of numbers x satisfying the give...
 1.1.18: In Exercises 1318, express the set of numbers x satisfying the give...
 1.1.19: In Exercises 1922, describe the set as a union of finite or infinit...
 1.1.20: In Exercises 1922, describe the set as a union of finite or infinit...
 1.1.21: In Exercises 1922, describe the set as a union of finite or infinit...
 1.1.22: In Exercises 1922, describe the set as a union of finite or infinit...
 1.1.23: Match (a)(f) with (i)(vi). (a) a > 3 (b) a 5 < 1 3 (c) a 1 3 < 5 ...
 1.1.24: Describe x : x x + 1 < 0 as an interval. Hint: Consider the sign of...
 1.1.25: Describe {x : x2 + 2x < 3} as an interval. Hint: Plot y = x2 + 2x 3.
 1.1.26: Describe the set of real numbers satisfying x 3=x 2 + 1 as a ha...
 1.1.27: Show that if a>b, and a, b = 0, then b1 > a1, provided that a and b...
 1.1.28: Which x satisfies both x 3 < 2 and x 5 < 1?
 1.1.29: Show that if a 5 < 1 2 and b 8 < 1 2 , then (a + b) 13 < 1. H...
 1.1.30: Suppose that x 4 1. (a) What is the maximum possible value of x ...
 1.1.31: Suppose that a 6 2 and b 3. (a) What is the largest possible va...
 1.1.32: Prove that xyx y. Hint: Apply the triangle inequality to y an...
 1.1.33: Express r1 = 0.27 as a fraction. Hint: 100r1 r1 is an integer. Then...
 1.1.34: Represent 1/7 and 4/27 as repeating decimals.
 1.1.35: The text states: If the decimal expansions of numbers a and b agree...
 1.1.36: Plot each pair of points and compute the distance between them: (a)...
 1.1.37: Find the equation of the circle with center (2, 4): (a) with radius...
 1.1.38: Find all points in the xyplane with integer coordinates located at...
 1.1.39: Determine the domain and range of the function f : {r, s, t, u}{A, ...
 1.1.40: Give an example of a function whose domain D has three elements and...
 1.1.41: In Exercises 4148, find the domain and range of the function. 41. f...
 1.1.42: In Exercises 4148, find the domain and range of the function.g(t) = t4
 1.1.43: In Exercises 4148, find the domain and range of the function.f (x) ...
 1.1.44: In Exercises 4148, find the domain and range of the function.g(t) =...
 1.1.45: In Exercises 4148, find the domain and range of the function.f (x) ...
 1.1.46: In Exercises 4148, find the domain and range of the function.h(s) =...
 1.1.47: In Exercises 4148, find the domain and range of the function.f (x) ...
 1.1.48: In Exercises 4148, find the domain and range of the function.g(t) =...
 1.1.49: In Exercises 4952, determine where f is increasing. f (x) = x + 1 5
 1.1.50: In Exercises 4952, determine where f is increasing. f (x) = x3
 1.1.51: In Exercises 4952, determine where f is increasing. f (x) = x4
 1.1.52: In Exercises 4952, determine where f is increasing. f (x) = 1 x4 + ...
 1.1.53: In Exercises 5358, find the zeros of f and sketch its graph by plot...
 1.1.54: In Exercises 5358, find the zeros of f and sketch its graph by plot...
 1.1.55: In Exercises 5358, find the zeros of f and sketch its graph by plot...
 1.1.56: In Exercises 5358, find the zeros of f and sketch its graph by plot...
 1.1.57: In Exercises 5358, find the zeros of f and sketch its graph by plot...
 1.1.58: In Exercises 5358, find the zeros of f and sketch its graph by plot...
 1.1.59: Which of the curves in Figure 26 is the graph of a function? (B) (C...
 1.1.60: Which of the curves in Figure 26 is the graph of a function? (B) (C...
 1.1.61: Determine whether the function is even, odd, or neither. (a) f (t) ...
 1.1.62: Write f (x) = 2x4 5x3 + 12x2 3x + 4 as the sum of an even and an od...
 1.1.63: Show that f (x) = ln 1 x 1 + x is an odd function.
 1.1.64: State whether the function is increasing, decreasing, or neither. (...
 1.1.65: In Exercises 6570, let f be the function shown in Figure 27. 65. Fi...
 1.1.66: Sketch the graphs of y = f (x + 2) and y = f (x) + 2.
 1.1.67: Sketch the graphs of y = f (2x), y = f 1 2 x , and y = 2f (x)
 1.1.68: Sketch the graphs of y = f (x) and y = f (x).
 1.1.69: Extend the graph of f to [4, 4] so that it is an even function.
 1.1.70: Extend the graph of f to [4, 4] so that it is an odd function. 1234...
 1.1.71: Suppose that f has domain [4, 8] and range [2, 6]. Find the domain ...
 1.1.72: Let f (x) = x2. Sketch the graph over [2, 2] of: (a) y = f (x + 1) ...
 1.1.73: Suppose that the graph of f (x) = sin x is compressed horizontally ...
 1.1.74: Figure 28 shows the graph of f (x) = x + 1. Match the functions (...
 1.1.75: Sketch the graph of y = f (2x) and y = f 1 2 x , where f (x) = x ...
 1.1.76: Find the function f whose graph is obtained by shifting the parabol...
 1.1.77: Define f (x) to be the larger of x and 2 x. Sketch the graph of f ....
 1.1.78: For each curve in Figure 30, state whether it is symmetric with res...
 1.1.79: Show that the sum of two even functions is even and the sum of two ...
 1.1.80: Suppose that f and g are both odd. Which of the following functions...
 1.1.81: Prove that the only function whose graph is symmetric with respect ...
 1.1.82: Prove the triangle inequality (a + ba+b) by adding the two in...
 1.1.83: Show that a fraction r = a/b in lowest terms has a finite decimal e...
 1.1.84: Let p = p1 ...ps be an integer with digits p1,...,ps. Show that p 1...
 1.1.85: A function f is symmetric with respect to the vertical line x = a i...
 1.1.86: Formulate a condition for f to be symmetric with respect to the poi...
Solutions for Chapter 1.1: Real Numbers, Functions, and Graphs
Full solutions for Calculus: Early Transcendentals  3rd Edition
ISBN: 9781464114885
Solutions for Chapter 1.1: Real Numbers, Functions, and Graphs
Get Full SolutionsThis textbook survival guide was created for the textbook: Calculus: Early Transcendentals , edition: 3. This expansive textbook survival guide covers the following chapters and their solutions. Calculus: Early Transcendentals was written by Patricia and is associated to the ISBN: 9781464114885. Chapter 1.1: Real Numbers, Functions, and Graphs includes 86 full stepbystep solutions. Since 86 problems in chapter 1.1: Real Numbers, Functions, and Graphs have been answered, more than 17170 students have viewed full stepbystep solutions from this chapter.

Additive inverse of a complex number
The opposite of a + bi, or a  bi

Augmented matrix
A matrix that represents a system of equations.

Basic logistic function
The function ƒ(x) = 1 / 1 + ex

Bounded below
A function is bounded below if there is a number b such that b ? ƒ(x) for all x in the domain of f.

Continuous function
A function that is continuous on its entire domain

General form (of a line)
Ax + By + C = 0, where A and B are not both zero.

Grapher or graphing utility
Graphing calculator or a computer with graphing software.

Infinite limit
A special case of a limit that does not exist.

Interval notation
Notation used to specify intervals, pp. 4, 5.

Irreducible quadratic over the reals
A quadratic polynomial with real coefficients that cannot be factored using real coefficients.

Linear function
A function that can be written in the form ƒ(x) = mx + b, where and b are real numbers

Multiplicity
The multiplicity of a zero c of a polynomial ƒ(x) of degree n > 0 is the number of times the factor (x  c) (x  z 2) Á (x  z n)

NDER ƒ(a)
See Numerical derivative of ƒ at x = a.

Principal nth root
If bn = a, then b is an nth root of a. If bn = a and a and b have the same sign, b is the principal nth root of a (see Radical), p. 508.

Quotient polynomial
See Division algorithm for polynomials.

Reciprocal identity
An identity that equates a trigonometric function with the reciprocal of another trigonometricfunction.

Reciprocal of a real number
See Multiplicative inverse of a real number.

Vertex of a cone
See Right circular cone.

Weights
See Weighted mean.

ycoordinate
The directed distance from the xaxis xzplane to a point in a plane (space), or the second number in an ordered pair (triple), pp. 12, 629.
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