Problem Solving Algebraic Expressions

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.

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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.