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You should be able to give a general description and aspecific example of each and a precise definition for those marked with an asterisk (*) .  \n The language of algebra is based on numbers and variables. These are combined in expressions, and two or more expressions connected by a verb make up an algebraic sentence.  \n Formulas are equations stating that a single variable is equal to an expression with one or more variables on the other side. Formulas are evaluated and can be rewritten using the rules for the order of operations and properties of equality.  \n A function is defined as a set of ordered pairs in which each first coordinate can be paired with exactly one second coordinate. The first coordinate of the ordered pair is the independent variable; the second coordinate is the dependent variable. Thus, a function pairs two variables in such a way that each value of the independent variable corresponds to exactly one value of the dependent variable. The domain of a function is the set of possible values for the independent variable, while the range is the set of values obtained for the dependent variable. Many functions are mathematical models of real situations or other mathematical properties.  \n Functions can be used to represent situations where one value of an ordered pair is known and the other unknown. They can also be used to describe situations in which objects are transformed or otherwise mapped onto other objects. Each of these types of situations may arise in everyday contexts and in all branches of mathematics.  \n Functions are often named with a single letter. Euler’sf(x) notation f(x) = x + 20, and the mapping notation f : x → x + 20, both describe the same function. Graphing utilities use f (x) notation and often name functions y 1, y2, y3, and so on. A CAS defines functions with f(x) notation, but also accepts equations and formulas that are not solved for one variable.  \nVocabulary  \n1-1  \n*variable algebraic expression expression algebraic sentence  \nevaluating an expression order of operations vinculum  \n*equation  \n*formula  \n1-2  \nrelation  \n*function  \n*independent variable  \n*dependent variable input, output  \nis a function of maps mathematical model 1-3  \n*f(x) notation argument of a function value of a function mapping notation  \n1-4  \nreal function  \n*domain of a function  \n*range of a function set builder notation trace  \nstandard window  \n*natural numbers  \n*counting numbers  \n*whole numbers  \n*integers rational numbers real numbers irrational numbers  \nChapter Wrap-Up  \n Along with words and formulas, functions are also represented by tables and graphs.  \nx y  \n–2 18  \nA sequence is a function whose domain is the set of all positive integers or the set of positive integers from a to b. Sequences may be defined with an explicit formula in which the nth term can be calculated directly from n. In a sequence S, the nth term isidentified as Sn.  \n Theorems and Properties   \nDistributive Property p. 41  \nOpposite of a Sum Theorem p. 44  \nVocabulary  \n1-7  \nequivalent formulas  \n1-8  \n*sequence  \nterm of a sequence subscript  \nindex  \n*explicit formula discrete function  \nSummary and Vocabulary 63  \nChapter 1  \nSelf-Test  \nTake this test as you would take a test in class. You will need a calculator. Then use the Selected Answers section in the back of the book to check your work.  \n1. Iff(x) = x2-4x, find f(–1 .5) to the nearest hundredth.  \n2. Suppose that f is a function and a is a real number. Describe the difference in the statements “f (a) = 7” and “f(7) = a.”  \n3. The table below defines the function g. Find g(–2) and g (2) .  \nIn 4 and 5, let f be the function graphed below.  \n4. Find the domain and range off.  \n5. Use the graph to estimate each of the following:  \na. f(3)  \nb. All values of x such that f(x) = 4.  \n6. Suppose S: n → (3(n-1)) . Evaluate S(10) .  \n7. Which formula","cbCaio3gArBlz2Py","https://ap.wps.com/l/cbCaio3gArBlz2Py","pdf",646984,"English","# Summary and Vocabulary\n## Theorems and Properties\n## Chapter Wrap-Up\n# Self-Test","[{\"question\":\"How are functions defined using ordered pairs, and what are independent and dependent variables?\",\"answer\":\"A function is defined as a set of ordered pairs where each first coordinate corresponds to exactly one second coordinate. The first coordinate is the independent variable and the second coordinate is the dependent variable.\"},{\"question\":\"What is the difference between f(a) = 7 and f(7) = a?\",\"answer\":\"In f(a) = 7, substituting a into the function gives an output of 7. In f(7) = a, substituting 7 gives an output equal to a.\"},{\"question\":\"How do sequences relate to functions, and how can the nth term be represented?\",\"answer\":\"A sequence is a function whose domain is the set of positive integers (or a subset from a to b). The nth term is identified as Sn, and sequences may be defined using an explicit formula that calculates the nth term directly from n.\"}]","Chapter 1 - Summary and Vocabulary - Self-Test | PDF",1790865895]