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Algebra 2 with Trig Chapter 2 Name______________________________ Mrs. McConnell Practice problems should be completed without the use of a calculator unless noted. The solutions are on Vision. This material will be featured on the next quiz. KNOW: 2.1 1. What is a relation? (in own words) 2. How can you find the domain and range from a relation, table, graph, or mapping? 3. Define function. 4. How to use the vertical line test. PRACTICE PROBLEMS (without a calculator): If f ( x) 2 x 2 4 x 1 , find: 1. f (2) 1 3 2. f ( 3) 3 4 4. f 3. f KNOW: 2.2 1. What is the slope formula? 2. How can you tell the difference between a line with a positive, negative, zero, or undefined slope? 3. What is the difference between lines that are parallel and perpendicular? PRACTICE PROBLEMS (without a calculator): #1-3 Find the slope between the two points. 1. (2, -4) (2, -3) 1 2 3 4 2. , 1 ,3 7 8 7 8 3. 2, 4, #4-5 Tell whether the lines are parallel, perpendicular, or neither. 4. Line 1: (3, -1) and (6, -4) Line 2: (-4, 5) and (-2, 7) 5. Line 1: (1, -4) and (4, -2) Line 2: (8, 1) and (14, 5) **#6-8 Find the value of k so that the line through the given points has the given slope. It helps to check your solution!! 6. (3, 1) (6, k ), m 2 5 7. (2k , 1) 3,5 , m 1 2 8. 3k , 2 (9, k ), m undefined KNOW: 2.3 How to graph lines: in slope-intercept form, standard form, horizontal lines, and vertical lines. KNOW: 2.4 1. Write equations of lines given a point and slope. 2. Write equations of lines given 2 points. 3. Write equations of lines given a graph. 4. Write equations of lines parallel or perpendicular to a given line. 5. Use slope-intercept form and point-slope form. 6. Rewrite equations in standard form. PRACTICE PROBLEMS Write the equations of the lines with the given information. Write answers in slope-intercept and standard form. 1. m 2, 2,7 2. (2, 9) (8,1) 3. (3, 5), parallel to y 4 x 1 4. (2,8), perpendicular to 4 x 3 y 9 5. (6, 2), perpendicular to y 5 KNOW: **(CALCULATORS ALLOWED)** 2.5 1. Use the model for direct variation. (Note: our book uses “a” for the constant of variation, but the SOL test and your teacher use “k.”) 2. WORD PROBLEMS!!!! PRACTICE PROBLEMS 1. Charles Law states that when pressure if constant, the volume, V, of a gas varies directly with its temperature, T (in kelvins). A gas occupies 4.8 liters at a temperature of 300 kelvins. A) Write an equation that gives V as a function of T. B) What is the volume of the gas when the temperature is 410 kelvins? 2. Hail 0.5 inch deep and weighing 1800 pounds covers a roof. The hail’s weight, w, varies directly with its depth, d. A) Write an equation that relates d and w. B) What is the weight on the “roof of hail” that is 1.75 inches deep? KNOW: 2.6 1. Difference between positive, negative, and no correlation when looking at a graph of a relation. KNOW: 2.8 1. How to graph linear inequalities 1. Graph: y 2 x4 3 2. Graph: 4 x 3 y 12