Algebra Know-It-ALL

which simplifies to y= 112,500 Jane’s share was therefore $112,500. Jack got the other portion, which was 1/3 of $112,500, or $3 ...

206 First-Degree Equations in One Variable Are you confused? Suppose you’re trying to solve a word problem, and you set up an eq ...

Practice Exercises This is an open-book quiz. You may (and should) refer to the text as you solve these problems. Don’t hurry! Y ...

208 CHAPTER 13 Mappings, Relations, and Functions When the elements of two sets are associated with each other in an organized w ...

Maximal domain and co-domain The large rectangles in Fig. 13-1 contain more points than those inside the ovals. The top rectangl ...

210 Mappings, Relations, and Functions that contains two items separated by a comma. The first item represents an element of the ...

the set of all positive rationals, and the lower oval represents the set of all negative rationals. Here’s the mapping: any numb ...

212 Mappings, Relations, and Functions in set X corresponds to one, but only one, element y in set Y. A mapping of this type is ...

Types of Mappings 213 Are you confused? In Fig. 13-3, the domain is shown as a proper subset of set X, and the range is shown as ...

214 Mappings, Relations, and Functions This mapping is an injection. The domain is the whole set X,and the range happens to be a ...

Examples of Relations Whenever you can express a mapping in terms of ordered pairs, then that mapping is a relation. The example ...

216 Mappings, Relations, and Functions When we plug specific values of the independent variable x into this equation, we get res ...

Are you confused? Graphs can make relations easier to understand. In the next chapter, you’ll learn about one of the most common ...

218 Mappings, Relations, and Functions can proceed in Fig. 13-8 along the dashed “square spiral,” increasing n by 1 each time we ...

This is another example of a function. If we call it g, we can write g(v)=v^2 For every value of v in the domain of g, there is ...

220 Mappings, Relations, and Functions Solution The inverse of g is not a function. Here’s the function again. Remember that the ...

Practice Exercises This is an open-book quiz. You may (and should) refer to the text as you solve these problems. Don’t hurry! Y ...

222 Mappings, Relations, and Functions z (that is, we divide 1 by z). If z= 0, we say that q is not defined. If we let z be the ...

223 CHAPTER 14 The Cartesian Plane In the 1600s, the French mathematician Rene Descartes (pronounced “re-NAY day-CART”) invented ...

224 The Cartesian Plane –6 –4 –2 246 2 4 6 –2 –4 –6 Negative independent- variable axis Positive dependent- variable axis Positi ...