Chapters 1–3 Cumulative Review Exercises 287 7. Graph each line by finding the x- and y-intercepts. a. 2x - y = 6 b. y = 1 5 x + 1 c. x + 3y = 0 8. The equation x = 5 is a line. 9. The equation y = -1 is a line. 10. Suppose an airplane descends at a rate of 400 ft/min from an altitude of 8000 ft above the ground. a. Write a linear equation that represents the plane’s altitude, y, after x min. b. Find the x-intercept and state its meaning. c. Find the y-intercept and state its meaning. 11. State the slope of each line. a. y = 4 5 x + 3 b. 3x + y = 9 c. x = 4 d. y = 7 e. Through (4, -1) and (6, 5) f. Parallel to y = 7x + 4 g. Perpendicular to y = -3x h. 2 y 2 4 4 6 –2 –4 –2 –4 x 12. Graph the line y=- 3 2 x + 4 using the slope and y-intercept. Label the y-intercept and at least one other point. 13. Determine if the lines 5x + 2y = 10 and 4x - 10y = -4 are parallel, perpendicular, or neither. 14. The equation y = 138.41x + 2961.8 models the average undergraduate cost of attending a public 2-yr college x years after 1986. (Source: http://nces.ed.gov/fastfacts) a. What are the slope and y-intercept? b. What do they mean in the context of this problem? c. Use this model to find the cost of attending a 2-yr college in 2016. 15. Write the equation of the line that satisfies the given conditions. a. m = 3 4 and passes through (0,-6) b. m = -2 and passes through (-7, 4) c. passes through (4, -1) and (6, 5) d. passes through (2, -8) and parallel to y = 4x - 1 e. passes through (3, 0) and perpendicular to y = -3x + 9 16. Suppose the enrollment of Einstein Community College was 16,000 in 1998 and 22,000 in 2004. If x is the number of years after 1998 and y is the college’s enrollment, write a linear equation that represents Einstein’s enrollment x years after 1998. 17. Which of the following relations is not a function? a. {(-2, 4), (-1, 1), (0, 0), (1, 1), (2, 4)} b. E(x, y)ux = person and y = person’s Social Security number.F c. d. 6 –4 –2 x 18. Find f (0) and f (-2) for f (x) = x2 - 3x + 2. 19. Write the linear equation 4x - 7y = -14 in function notation. Then find f (-14). Write the corresponding ordered pair. 20. Explain what it means for a relation to be a function. Provide a real-life example of a function. 2 4 4 –2 y 2 2 6 4 –2 –2 –4 x y CUMULATIVE REVIEW EXERCISES / CHAPTERS 13 1. Evaluate each absolute value expression. (Section 1.1, Objective 5) a. |6| b. `- 3 4 ` c. -u-24u 2. Perform the each operation and simplify each result. (Section 1.2, Objectives 2–7) a. 15 16 + 7 12 - 17 18 b. 6 2 5 · 3 3 4 ÷ 12 c. 4 1 5 - 1 2 3 + 4 15 3. Use the order of operations to simplify each numerical expression. (Section 1.3, Objectives 1 and 2) a. - a- 3 2 b 3 b. 1 6 (10 - 8)3 - 5 3 c. 2(7)2 - 5(12) + 1 d. 520 - 2u13 - 2(4 - 1) u 13 + 1132 + 5(13)(6) e. 2 · 6 4. Evaluate each expression for the given values of the variables. (Section 1.3, Objective 3) a. 2x + 3 x - 1 for x = 0, 1, 2, 3 b. b2 - 4ac for a = 5, b = 2, c = 15
hendricks_beginning_algebra_1e_ch1_3
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