4 Find the Domain of a Function Using Its Equation We have seen how to determine the domain of a relation written as a set of ordered pairs, as a correspondence (or mapping), and as a graph. Next, we will discuss how to determine the domain of a relation written as an equation. Sometimes, it is helpful to ask yourself, “Is there any number that cannot be substituted for x?” EXAMPLE 4 In-Class Example 4 Determine the domain of each function. a) y 6x 9 b) y x3 c) y 1 x Answer: a) (q, q) b) (q, q) c) (q, 0) ´ (0, q) Determine the domain of each function. a) y 3x 1 b) y x2 c) y 1 x Solution a) To determine the domain of y 3x 1, ask yourself, “Is there any number that cannot be substituted for x?” No. Any real number can be substituted for x, and y 3x 1 will be defi ned. The domain consists of all real numbers and can be written as (q, q). b) Ask yourself, “Is there any number that cannot be substituted for x in y x2?” No. Any real number can be substituted for x. The domain is all real numbers, (q, q). c) To determine the domain of y 1 x , ask yourself, “Is there any number that cannot be substituted for x?” Yes. x cannot equal zero because a fraction is undefi ned if its denominator equals zero. Any other number can be substituted for x and y 1 x will be defi ned. The domain consists of all real numbers except 0. We can write the domain in interval notation as (q, 0) ´ (0, q). Procedure Finding the Domain of a Function To fi nd the domain of a function written as an equation in terms of x: 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. YOU TRY 3 Determine the domain of each function. a) y x 8 b) y x2 3 c) y 5 x 2 644 CHAPTER 10 Quadratic Equations www.mhhe.com/messersmith
messersmith_power_introductory_algebra_1e_ch4_7_10
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