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Unformatted text preview: tion (equation) that defines two or more particular (x,y) pairs (members of the domain set and corresponding members of the range set). These questions sometimes involve real-life situations; you may be asked to construct a mathematical “model” that defines a relationship between, for example, the price of a product and the number of units of that product. The graph of a particular linear function on the xy-plane A linear function that defines a particular line on the xy-plane. • • Variations on the latter two types of problems may involve determining the slope and/or y-intercept of a line defined by a function, or identifying a function that defines a given slope and y-intercept. Example: In the linear function f, if f(–3) = 3 and if the slope of the graph of f in the xy-plane is 3, what is the equation of the graph of f ? (A) y = 3x – 3 (B) y = 3x + 12 (C) y=x–6 (D) y = –x (E) y = 3 x – 12 Solution: The correct answer is (B). In the general equation y = mx + b, slope (m) is given as 3. To determine b, substitute –3 for x and 3 for y, then solve for b: 3 = 3(–3) + b; 12 = b. Only in choice (B) does m = 3 and b = 12. www.petersons.com Numbers and Operations, Algebra, and Functions 257 Exercise 7
Work out each problem. Circle the letter that appears before your answer. 1. XYZ Company pays its executives a starting salary of $80,000 per year. After every two years of employment, an XYZ executive receives a salary raise of $1,000. Which of the following equations best defines an XYZ executive’s salary (S) as a function of the number of years of employment (N) at XYZ? (A) (B) (C) (D) (E) 2.
S= 1, 000 + 80, 000 N 4. In the xy-plane below, if the scales on both axes are the same, which of the following could be the equation of a function whose graph is l1 ? S = N + 80,000
S= 80, 000 + 1, 000 N S = 1,000N + 80,000 S = 500N + 80,000 (A) (B) (C) (D) (E) 5. y= 2 x–3 3 y = –2x + 1 y=x+3 y = –3x −
2 3 In the linear function g, if g(4) = –9 and g(–2) = 6, what is the y-intercept of the graph of g in the xy-plan...
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This note was uploaded on 08/15/2010 for the course MATH a4d4 taught by Professor Colon during the Spring '10 term at Embry-Riddle FL/AZ.
- Spring '10