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# Solutions for Chapter 6: TRANSFORMATIONS OF FUNCTIONS AND THEIR GRAPHS

## Full solutions for Functions Modeling Change: A Preparation for Calculus | 4th Edition

ISBN: 9780470484753

Solutions for Chapter 6: TRANSFORMATIONS OF FUNCTIONS AND THEIR GRAPHS

Solutions for Chapter 6
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##### ISBN: 9780470484753

Functions Modeling Change: A Preparation for Calculus was written by and is associated to the ISBN: 9780470484753. This expansive textbook survival guide covers the following chapters and their solutions. Since 45 problems in chapter 6: TRANSFORMATIONS OF FUNCTIONS AND THEIR GRAPHS have been answered, more than 40285 students have viewed full step-by-step solutions from this chapter. Chapter 6: TRANSFORMATIONS OF FUNCTIONS AND THEIR GRAPHS includes 45 full step-by-step solutions. This textbook survival guide was created for the textbook: Functions Modeling Change: A Preparation for Calculus , edition: 4.

Key Calculus Terms and definitions covered in this textbook
• Additive identity for the complex numbers

0 + 0i is the complex number zero

• Arc length formula

The length of an arc in a circle of radius r intercepted by a central angle of u radians is s = r u.

• Boundary

The set of points on the “edge” of a region

• Completing the square

A method of adding a constant to an expression in order to form a perfect square

• Convergence of a sequence

A sequence {an} converges to a if limn: q an = a

• Elementary row operations

The following three row operations: Multiply all elements of a row by a nonzero constant; interchange two rows; and add a multiple of one row to another row

• Fitting a line or curve to data

Finding a line or curve that comes close to passing through all the points in a scatter plot.

• Geometric series

A series whose terms form a geometric sequence.

• Imaginary unit

The complex number.

• Infinite sequence

A function whose domain is the set of all natural numbers.

• Inverse tangent function

The function y = tan-1 x

• Linear factorization theorem

A polynomial ƒ(x) of degree n > 0 has the factorization ƒ(x) = a(x1 - z1) 1x - i z 22 Á 1x - z n where the z1 are the zeros of ƒ

• Linear inequality in two variables x and y

An inequality that can be written in one of the following forms: y 6 mx + b, y … mx + b, y 7 mx + b, or y Ú mx + b with m Z 0

• Logistic growth function

A model of population growth: ƒ1x2 = c 1 + a # bx or ƒ1x2 = c1 + ae-kx, where a, b, c, and k are positive with b < 1. c is the limit to growth

• Lower bound of f

Any number b for which b < ƒ(x) for all x in the domain of ƒ

• Measure of an angle

The number of degrees or radians in an angle

• Numerical model

A model determined by analyzing numbers or data in order to gain insight into a phenomenon, p. 64.

• Sample space

Set of all possible outcomes of an experiment.

• Sum of an infinite geometric series

Sn = a 1 - r , |r| 6 1

• Vertex of an angle

See Angle.