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messersmith_power_intermediate_algebra_1e_ch4_7_10

y 7 x 3 is a function. For every value that can be substituted for x there is only one corresponding value of y. c) Is there any number that cannot be substituted for x in y 2x 6? No. Any real number can be substituted for x, and y 2x 6 will be defi ned. The domain consists of all real numbers which can be written as (q, q). Every value substituted for x will have exactly one corresponding y-value. y 2x 6 is a function. YOU TRY 4 Determine the domain of each relation, and determine whether each relation Remember that only when a relation is classified as a function, do we replace y with f(x). Procedure Finding the Domain of a Relation The domain of a relation that is written as an equation, where y is in terms of x, is the set of all real numbers that can be substituted for the independent variable, x. When determining the domain of a relation, it can be helpful to keep these tips in mind. 1) Ask yourself, “Is there any number that cannot be substituted for x?” 2) If x is in the denominator of a fraction, determine what value of x will make the denominator equal 0 by setting the expression equal to zero. Solve for x. This x-value is not in the domain. The domain consists of all real numbers that can be substituted for x. describes y as a function of x. a) y x 9 b) y x2 6 c) y 4 x 1 3 Use Function Notation We can use function notation to name functions. If a relation is a function, then f (x) can be used in place of y. In this case, f (x) is the same as y. For example, y x 3 is a function. We can also write y x 3 as f (x) x 3. They mean the same thing. Definition y f (x) is called function notation, and it is read as “y equals f of x.” y f (x) means that y is a function of x ( y depends on x). www.mhhe.com/messersmith SECTION 4.5 Introduction to Functions 203


messersmith_power_intermediate_algebra_1e_ch4_7_10
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