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Algebra II with Trigonometry Name______________________________ Chapter 2 Review Test Tues 11/19/10 1) Consider the relation { (-8, 8), (-5, 5), (-2, 2), (0, 0), (4, 4), (7, 7) }. State the domain. ________________ State the range. ________________ What is the rule? _________ Is the relation a function? _____ Why or why not? 2) If f(x) = 3x - 5 and g(x) = x2, find f(g(-4)). _______ 3) If the domain of the function f(x) = -3x2 – 2x is {-6, -2, 4}, what is the range for the function? ______________ 4) Find the slope of the line containing the points (3, -1) and (-6, -4). __________ 5) Write the equation 4x – 3y = 18 in slope-intercept form. State the slope.______ State the y-intercept.______ 6) For the equation 5x – 4y = 20, the x-intercept is ________ and the y-intercept is________. 7) Write the equation y = -2/5 x + 3/2 in standard form. ____________________ 8) Show whether or not the ordered pair (-3, 7) is a solution of the inequality 7x – 9y < -10. 9) Line #1 contains (2, -4) and (0, 2). Line #2 contains (-4, 5) and (-1, 6). Are the lines parallel, perpendicular, or neither? Explain. 10) Find the vertex for the graph of y = | 3x – 6 | + 5. ______________ GD/MPH/RS/CR 11/06 1 Algebra II with Trigonometry Write the equation of the line for the following: Slope-intercept form Standard form General form 11) Parallel to the x-axis through the point (-4, -7). 12) For the horizontal line passing through the point (5, 3). 13) Containing the points (3, 5) and (-3, 7). 14) Through origin with slope -2. 15) Has x-intercept 5 and y-intercept -11. GD/MPH/RS/CR 11/06 2 Algebra II with Trigonometry 16) With slope -2/3 and passing through the point (-3, 6). 17) Parallel to the line y = -3x + 1 and through the point (4, -3). 18) Perpendicular to the line y = -3x + 1 and through the point (4, -3). Solve to find the missing variable. 4 19) A line has a slope of and contains the points (1, -7) and (9, y). 3 What is the value of y? Determine the rate of change. 20) In 1992 Bob earned $35,460 per year and he now earns $59,200. What is the rate of change for Bob’s salary per year? GD/MPH/RS/CR 11/06 3 Algebra II with Trigonometry Sketch the graphs of the following using x and y-intercepts. 21) x – y = -4 22) 3x + 8y = 24 Sketch the graphs of the following. 23) -4x > 20 GD/MPH/RS/CR 11/06 24) 3y – 2x < -6 4 Algebra II with Trigonometry Sketch the graphs of the following. Label the vertex and 2 other points on the graph. 25) y = | x + 6 | 26) y = - | x | + 4 27) y = - | x - 5 | GD/MPH/RS/CR 11/06 28) y = | x + 3 | - 5 5 Algebra II with Trigonometry Scientists record data from experiments with hope of eventually finding patterns that will enable them to predict future results. For example, in testing an antibacterial ointment, a chemist might record the number of bacteria present in a tissue culture after using the ointment for different periods of time. The table below shows a record of the number of hours and the number of bacteria. Make a scatter plot of this data. Does there appear to be a relationship between time and the effectiveness of the ointment (positive, negative, or no correlation)?__________________________ Use the scatter plot to support your answer. Find the slope of the line of best fit of the data. __________ What is the meaning of slope for the data? After how many hours do you expect one-half of the bacteria to be terminated?___________ Do you expect that all the bacteria will be terminated?____________ Why or why not? GD/MPH/RS/CR 11/06 6 Algebra II with Trigonometry Chapter 2 Review ANSWERS 1) 1 x6 3 x + 3y = 18 x + 3y – 18 = 0 {-8, -5, -2, 0, 4, 7} {8, 5, 2, 0, 4, 7} y=|x| Yes 13) y = 2) 43 3) {-96, -56, -8} 14) y = -2x 2x + y = 0 2x + y = 0 4) 1 3 5) m= 4 3 y-int (0, -6) 11 x 11 5 11x - 5y = 55 11x – 5y – 55 = 0 13.5 hours 2 x4 3 2x + 3y = 12 2x + 3y – 12 = 0 7) 4x + 10y = 15 8) Yes 17) y = -3x + 9 3x + y = 9 3x + y – 9 = 0 9) Perpendicular 18) y = 1 13 x 3 3 x – 3y = 13 x – 3y – 13 = 0 10) (2, 5) GD/MPH/RS/CR 11/06 m = -2.95 Decrease of 3 bacteria per hour 16) y = x-int (4, 0) y-int (0, -5) 12) y = 3 y=3 y–3=0 Negative correlation 15) y = 6) 11) y = -7 y = -7 y+7=0 Scatter Plot 19) 53 3 20) Increase of $1318.89 per year 7