12/15/2023 0 Comments College calculus examplesSince there is no real number with a square that is negative, the negative real numbers are not elements of the range. Since every nonnegative real number has a real-value square root, every nonnegative number is an element of the range of this function. Then, the input x = 3 x = 3 is assigned to the output 3 2 = 9. The set of outputs is called the range of the function.įor example, consider the function f, f, where the domain is the set of all real numbers and the rule is to square the input. The set of inputs is called the domain of the function. Since functions have so many uses, it is important to have precise definitions and terminology to study them.Ī function f f consists of a set of inputs, a set of outputs, and a rule for assigning each input to exactly one output. The cost of mailing a package is a function of the weight of the package. The velocity of a ball thrown in the air can be described as a function of the amount of time the ball is in the air. For example, the area of a square is determined by its side length, so we say that the area (the output) is a function of its side length (the input). For any function, when we know the input, the output is determined, so we say that the output is a function of the input. Functions are used all the time in mathematics to describe relationships between two sets. The element of the first set is called the input the element of the second set is called the output. A function is a special type of relation in which each element of the first set is related to exactly one element of the second set. A relation from A A to B B defines a relationship between those two sets. Given two sets A A and B, B, a set with elements that are ordered pairs ( x, y ), ( x, y ), where x x is an element of A A and y y is an element of B, B, is a relation from A A to B. Most of this material will be a review for you, but it serves as a handy reference to remind you of some of the algebraic techniques useful for working with functions. We also define composition of functions and symmetry properties. We study formal notation and terms related to functions. In this section, we provide a formal definition of a function and examine several ways in which functions are represented-namely, through tables, formulas, and graphs.
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