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messersmith_power_intermediate_algebra_1e_ch4_7_10

Definition/Procedure Example Determine the domain of f (x) 9 x 8 . x 8 0 Set the denominator 0. x 8 Solve. When x 8, the denominator of f (x) 9 x 8 equals zero. The domain contains all real numbers except 8. The domain of the function is (q, 8) ´ (8, q). If f (x) 9x 4, fi nd f (2). Substitute 2 for x and evaluate. f(2) 9(2) 4 18 4 14 f(2) 14 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 denominator equal to zero. Solve for x. This x-value is not in the domain. (p. 203) Function Notation If a function describes the relationship between x and y so that x is the independent variable and y is the dependent variable, then y is a function of x. y f (x) is called function notation and it is read as “y equals f of x.” Finding a function value means evaluating the function for the given value of the variable. (p. 203) A linear function has the form f (x) mx b where m and b are real numbers, m is the slope of the line, and (0, b) is the y-intercept. (p. 206) Graph f (x) 3x 4 using the slope and y-intercept. The slope is 3 and the y-intercept is (0, 4). Plot the y-intercept, and use the slope to locate another point on the line. x 5 (0, 4) 5 5 5 (1, 1) (x) 3x 4 Chapter 4: Review Exercises (4.1) Determine whether each ordered pair is a solution of the given equation. 1) 4x y 9; (1, 5) 2) 3x 2y 20; (4, 2) 3) y 5 4 x 1 2 ; (2, 3) 4) x 7; (7, 9) Complete the ordered pair for each equation. 5) y 6x 10; (3, ) 6) y 2 3 x 5; (12, ) 7) y 8; (5, ) 8) 5x 9y 3; ( , 2) Complete the table of values for each equation. 9) y x 11 10) 4x 6y 8 x y 0 3 1 5 x y 0 0 3 4 www.mhhe.com/messersmith CHAPTER 4 Review Exercises 221


messersmith_power_intermediate_algebra_1e_ch4_7_10
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