Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 1- 1 Homework, Page 124 Find the formulas for f + g, f – g, and fg. Give the domain of each. 1.

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 1- 2 Homework, Page 124 Find the formulas for f / g, and g / f. Give the domain of each. 5.

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 1- 3 Homework, Page and are shown in a[0. 5] by [0, 5] viewing window. Sketch the graph of the sum

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 1- 4 Homework, Page 124 Find and 13.

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 1- 5 Homework, Page 124 Find and and find the domain of each. 17.

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 1- 6 Homework, Page 124 Find and and find the domain of each. 21.

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 1- 7 Homework, Page 124 Find and so that the function can be described as. 25.

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 1- 8 Homework, Page 124 Find and so that the function can be described as. 29.

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 1- 9 Homework, Page A satellite camera takes a rectangular- shaped picture. The smallest region that can be photographed is a 5-km by 7-km rectangle. As the camera zooms out, the length and width of the rectangle increase at the rate of 2 km/sec. How long does it take for the area A to be at least five times the original size?

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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Homework, Page 124 Find two functions defined implicitly by the given relations. 37.

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Homework, Page 124 Find two functions implicitly defined by the given relations. 41.

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Homework, Page True or False. The domain of the quotient function consists of all numbers that belong to both the domain of f and the domain of g. Justify your answer. False. The domain of the quotient function consists of all numbers that belong to both the domain of f and the domain of g, less those that result in.

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Homework, Page If, then a.b. c.d. e.

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Homework, Page An identity for a function operation is a function that combines with a given function f to return the same function f. Find the identity functions for the following operations. a. Find a function g such that b. Find a function g such that c. Find a function g such that

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Homework, Page a. Find a function g such that b. Find a function g such that

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Homework, Page c. Find a function g such that

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 1.5 Parametric Relations and Inverses

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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide What you’ll learn about Defining Relations Parametrically Inverse Relations Inverse Functions … and why Some functions and graphs can best be defined parametrically, while some others can be best understood as inverses of functions we already know.

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Parametric Equations A parametric equation is one that defines the two elements of an ordered pair in terms of a third variable, called the parameter. A pair of parametric equations may define either a function or a relation. Remember, a function is a relation that passes the vertical line test.

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Example Defining a Function Parametrically

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Example Defining a Function Parametrically

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Inverse Relation The ordered pair (a,b) is in a relation if, and only if, the pair (b,a) is in the inverse relation.

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Horizontal Line Test The inverse of a relation is a function if, and only if, any horizontal line intersects the graph of the original relation at no more than one point. A function that passes this horizontal line test is called a one-to-one function.

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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide The Inverse Reflection Principle The points (a, b) and (b, a) in the coordinate plane are symmetric with respect to the line y = x. The points (a, b) and (b, a) are reflections of each other across the line y = x.

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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Homework Homework Assignment #5 Review Section 1.6 Page 135, Exercises: 1 – 49 (EOO), skip 45 Quiz next time

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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide What you’ll learn about Transformations Vertical and Horizontal Translations Reflections Across Axes Vertical and Horizontal Stretches and Shrinks Combining Transformations … and why Studying transformations will help you to understand the relationships between graphs that have similarities but are not the same.

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Transformations Rigid transformation – an action that changes a graph in a predictable manner. The shape and the size of the graph remain unchanged, but its position changes horizontally, vertically or diagonally. Non-rigid transformation – generally a distortion of the shape of a graph, including horizontal or vertical stretches and shrinks

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Translations Let c be a positive real number. Then the following transformations result in translations of the graph of y=f(x). Horizontal Translations y=f(x-c)a translation to the right by c units y=f(x+c)a translation to the left by c units Vertical Translations y=f(x)+ca translation up by c units y=f(x)-ca translation down by c units

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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Example Finding Equations for Translations

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Reflections The following transformations result in reflections of the graph of y = f(x): Across the x-axis y = – f(x) Across the y-axis y = f(– x)

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Graphing Absolute Value Compositions Given the graph of y = f(x), the graph y = |f(x)| can be obtained by reflecting the portion of the graph below the x-axis across the x-axis, leaving the portion above the x-axis unchanged; the graph of y = f(|x|) can be obtained by replacing the portion of the graph to the left of the y-axis by a reflection of the portion to the right of the y-axis across the y-axis, leaving the portion to the right of the y-axis unchanged. (The result will show even symmetry.)

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Compositions With Absolute Value Match the compositions of y = f(x) with the graphs a.b.c. d.e.f.

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Stretches and Shrinks Let c be a positive real number. Then the following transformations result in stretches or shrinks of the graph y = f(x). Horizontal Stretches or Shrinks Vertical Stretches and Shrinks

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