Chapter 3 Study Guide

Chapter 3 Study Guide Algebra 1 Determine whether the relation is a function. If the relation is a function, determine whether the function is linear or nonlinear. Explain. 1. 1   | x | y | |---|---| | -6 | 0 | | -1 | 1 | | 0 | 2 | | 1 | 2 | | 2 | 4 | Not a function. Since there is more than one output for the input x = 1. 2. y = -2x + 3 Function. Linear. There is a constant rate of change of -2 down 2. 3. x = -2 Not a Function. There are several outputs for the input x = -2. Graph the equation and identify the intercepts(s). If the equation is linear, find the slope of the line. 4. 2x - 3y = 6 2(0) - 3y = 6 0 - 3y = 6 -3y = 6 y = -2 2x - 3(0) = 6 2x = 6 x = 3 5. y = 4.5 memorize all points y = 4.5 6. y = |x - 1| - 2 V-shape down 2 right 1 center (1, -2) Find the domain and the range of the function represented by the graph. Determine whether the domain is discrete or continuous. Explain. 7. D: all reals (→ forever) R: all reals (↑ forever) Continuous (connected) 8. D: {-2, -1, 0, 1, 2, 3} R: {-8, -5, -2, 1, 5, 7} Discrete (dots) we only have whole #s Graph f and g. Describe the transformations from the graph of f to the graph of g. 9. f(x) = |x|; g(x) = |x| - 2 down 2 10. f(x) = |x|; g(x) = |x + 1| + 3 left 1 up 3 11. Solve: a) 4x - 9 = 1/4x + 2 4(4x - 9) = (4)(1/4x + 2) 16x - 36 = x + 8 15x = 44 x = 44/15 b) |3x - 7| = 8 3x - 7 = 8 or 3x - 7 = -8 3x = 15 or 3x = -1 x = 5 or x = -1/3 When solving absolute values, remember to always get two answers. 12. A mountain climber is scaling a 500-foot cliff. The graph shows the elevation of the climber over time. a) Find and interpret the slope and the y-intercept of the graph. 1   The climber started at 50 ft high on the cliff. The climber is climbing at a rate of 125 feet per hour. b) Explain two ways to find f(3). Then find f(3) and interpret the meaning. Plug into the equation f(3) = 125(3) + 50 and then solve or go to where x = 3 and find where it hits the graph f(3) = 425 3 hrs of climbing, he is 425 ft high on the cliff. c) How long does it take the climber to reach the top of the cliff? Justify your answer. It takes the climber 3.6 hours to reach the top. Using the graph, the feet 500 is on the line when x = 3.6 13. Without graphing, compare the slopes and the intercepts of the functions f(x) = x + 1 and g(x) = |2x + 1| • both have an intercept of 1 • the g(x) slope is twice as much as the f(x) slope. g(x) = 2x + 1