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Extra resources for Advanced Mathematical Concepts: Precalculus with Applications
C. Graph the function. 24 Chapter 1 Linear Relations and Functions 38. Critical Thinking How is the slope of a linear function related to the number of zeros for the function? 39. Economics Economists call the relationship between a nation’s disposable income and personal consumption expenditures the marginal propensity to consume or MPC. 70. That is, 70% of each additional dollar earned is spent and 30% is saved. a. Suppose a nation’s disposable income, x y x,and personal consumption (billions of (billions of expenditures, y, are shown in the table dollars) dollars) at the right.
Dept. of Commerce Lesson 1-6 Modeling Real-World Data with Linear Functions 41 5. Education Do you share a computer at school? The table shows the average number of students per computer in public schools in the United States. Students per Computer Academic Year 1983– 1984– 1984–1985– 1985– 1986– 1986– 1987– 1987– 1988– 1988– 1989– 1989– 1990– 1990– 1991– Average 125 75 50 37 32 25 22 20 Academic Year 1991– 1992– 1992– 1993– 1993– 1994– 1994– 1995– 1995– 1996– 1996– 1997– ? 8 1 Source: QED’s Technology in Public Schools E XERCISES l Wor ea Complete parts a–d for each set of data given in Exercises 6–11.
Assuming a linear relationship, find the average annual rate of increase. b. Explain how the rate is related to the graph of the line. 32. If f(x) ϭ x3 and g(x) ϭ 3x, find g[f(Ϫ2)]. (Lesson 1-2) f 33. Find (f и g)(x) and ᎏᎏ (x) for f (x) ϭ x3 and g(x) ϭ x2 Ϫ 3x ϩ 7. (Lesson 1-2) g 34. Given that x is an integer, state the relation representing y ϭ x2 and Ϫ4 Յ x Յ Ϫ2 by listing a set of ordered pairs. Then state whether this relation is a function. (Lesson 1-1) If xy ϭ 1, then x is the reciprocal of y.