When two variables r and A are related in this manner, it is customary to use the phrase A is a function of r.To cite another example, if an automobile travels at a uniform rate of 50 miles per hour, then the distance d (miles) traveled in time t (hours) is given by d = 50t and hence the distance d is a function of time t.Click "Show Answer" underneath the problem to see the answer.Tags: Media Analysis Essay QuestionsDe Havilland Essay PurchasingSpartacus And The Slave Wars EssayApa Format For DissertationEssay On Strengths And Weaknesses For MbaSchool Uniform Discursive EssayEdit My Essay For Free OnlineResearch Paper Plagiarism CheckerWriting Essay Childhood ObesityEssay Autobiography Coin
The notion of correspondence is encountered frequently in everyday life.
For example, to each book in a library there corresponds the number of pages in the book.
The element y is called the image of x under f and is denoted by f(x). The range of the function consists of all images of elements of X.
Earlier, we introduced the notation f(x) for the element of Y which corresponds to x.
Since the square of any real number is nonnegative.
T is contained in the set of all nonnegative real numbers.For each book x in X there corresponds a positive integer y, namely the number of pages in the book.In the second example, if we let X denote the set of all human beings and Y the set of all possible dates, then to each person x in X there corresponds a birth date y. Our examples indicate that to each x in X there corresponds one and only one y in Y; that is, y is unique for a given x.The letter r, which represents an arbitrary number from the domain off, is often called an independent variable.The letter A, which represents a number from the range off, is called a dependent variable, since its value depends on the number assigned tor.In much of our work X and Y will be sets of real numbers.To illustrate, let X and Y both denote the set R of real numbers, and to each real number x let us assign its square x.The curved arrows indicate that the elements f(x), f(w), f(z), and f(a) of Y correspond to the elements x, y, z and a of X.Let us repeat the important fact that to each x in X there is assigned precisely one image f(x) in Y; however, different elements of X such as w and z in Figure 1.18 may have the same image in Y. However, f(x) is an element of Y, namely the element which f assigns to x.You can review your answers and change them by checking the desired letter.Once you have finished, press "finish" and you get a table with your answers and the right answers to compare with.