TEST A CHAPTER 7, FUNCTIONS AND GRAPHS

Transcription

1 TEST A CHAPTER 7, FUNCTIONS AND GRAPHS. Find the domain and range of the relation R = {(, -), (, -), (, )}.. Find the domain and range of the relation R = {(x, y) y = x}.. Find the domain and range of the relation R = {(x, y) y < x, x and y positive integers less than 6}.. Which of the following relations is (are) functions? a. {(x, y) y = x + } b. {(x, y) y = x + } c. {(, ), (, ), (, )}. A function is defined by f(x) = x - x. Find: a. f() b. f() c. f(-) 6. The daily cost for renting a car ($ per day plus $. per mile) is given by C(m) = +.m, where m is the number of miles driven. If a person paid $.7 for one day's rental, how many miles did the person drive? 7. Graph the relation R = {(x, y) y = x, x a n integer between - and, inclusive}. ± ± ± ± ± ± ±

2 8. Graph the relation Q = {(x,y) x + y <, x and y nonnegative integers}. ± ± ± ± ± ± ± 9. Graph the function defined by g(x) = x -, x an integer and - < x <. ± ± ± ± ± ± ±. Graph the function defined by f(x) = - x ± ± ± ± ± ± ±

3 . Graph the equation x - y = - 6. ± ± ± ± ± ± ±. Find the distance between the two points: a. (, ), (, -) b. (7, -), (7, -). Find the slope of the line that goes through the two points (-, ) and (-, -).. Find the general equation of the line in Problem.. a. Find the slope-intercept form of the equation of the line that goes through the point (-, ) and has slope -. b. Find the slope-intercept form of the line x + y = 8. What is the slope and what is the y-intercept? 6. Determine whether or not the two given lines are parallel. If they are not parallel, find the coordinates of the point of intersection. a. x - y = 7, y = 6x - b. y = - x, 6x + y = 9 7. Find the general equation of the line that passes through the point (, ) and is parallel to the line x + y = Find the point of intersection of the lines x + y = 6 and x - y =.

4 9. Graph the solution set of the inequality y - x 6. ± ± ± ± ± ± ±. Graph the solution set of the system o f inequalities: x + y > 6 and x + y ± ± ± ± ± ± ±. Graph the solution set of the system o f inequalities: x + y, x y, y ± ± ± ± ± ± ±. Solve the following system if possible. If not possible, explain why y = x - 9x - y = 6

5 . Find the maximum value of C = x + y subject to the constraints: x + y > 6, x, and y. Find the minimum value of P = x - y subject to the constraints: x - y, x + y, x, y. Two machines produce the same item. Machine A can produce items per hour and machine B can produce items per hour. At least of the items must be produced each -hour week, but the machines cannot be operated at the same time. If it costs $ per hour to operate A and $ per hour to operate B, determine how many hours per week to operate each machine to meet the production requirement at minimum machine cost. 6. Graph y = - (x + ) - ± ± ± ± ± ± ± 7. Graph y = x + x + and give the coordinates of the vertex ± ± ± ± ± ± ±

6 8. Graph f(x) = x and g(x) = coordinate axes x on the same ± ± ± ± ± ± ± 9. Graph f(x) = e x and g(x) = ln x on the same coordinate axes ± ± ± ± ± ± ±. P dollars accumulate to the amount A = Pe rt when invested at a rate r for t years. If the interest rate is %, how long would it take for the money to double?

7 TEST B CHAPTER 7, FUNCTIONS AND GRAPHS. The domain of the relation R = {(, ), (, -), (, -)} is a. {-, -, } b. {,, } c. {-, -,,, } d. {-, -,,,, } e. None of these. The range of the relation R = {(x, y) y = x} is a. The positive real numbers b. The positive integers c. The integers d. The real numbers. The range of the relation {(x,y) y < x, x and y positive integers less than 6} is a. {,,,, } b. {,,, } c. {,, } d. {, } e. {}. Which of the following relations are functions? a. {(x, y) y = x + } b. {(x, y) y = x + } c. {(, ), (, ), (, )} a. a only b. b only c. b and c only d. a and b only. If a function is defined by f(x) = x - x, then f() equals a. 6 b. c. 8 d. x - x e. 6. The daily cost of renting a car is C(m) = +.m dollars, where m is the number of miles driven. If a person paid $.7 for one day's rental, the number of miles the person drove is a. 7 b. 7 c. d. e. 7. The graph of R = {(x, y) y = -x, x an integer between - and, inclusive} is a. b. c. d

8 8. The graph of the relation Q = { (x,y) x + y, x and y nonnegative integers} is a. b. c. d. 9. The graph of the function defined by g(x) = x -, x an integer and - < x < is a. b. c. d The graph of f(x) = - x is a. b. c. d The graph of the equation x - y = -6 is a. b. c. d

9 . The distance between (, ) and (, -) is a. b. 8 c. -6 d.. The slope of the line through (-, ) and (-, -) is a. / b. -/ c. d. -. The general equation of the line through (, ) and (-, ) is a. -x - y = 7 b. x + y = 7 c. x + y = -7 d. x - y = 7. The slope and the y-intercept of the line x - y = - are, respectively, a. /, - b. /, - c. /, d. /, 6. Which of the following lines are parallel?. y = - x. 6x - y = 9. 8x + y = 9 a. and only b. and only c. and only d. All three are parallel. 7. The general equation of the line passing through the point (, ) and parallel to the line x - y = - is: a. y - = (x - ) b. y = x c. x - y = d. y - = -(x - ) e. -x + y = Find the point of intersection (if there is one) of the lines x - y = 7 and y = 6x - a. (, ) b. (-, ) c. (-, -) d. (, -) e. There is none. 9. The graph of the solution set of y - x 6 is a. b. c. d

10 . The graph of the solution set of the system of inequalities x + y 6 and x + y > is: a. b. c. d. x+y= -6 6 x+y=6 6 x+y=6 6 x+y=6 6 x+y= x+y= x+y= x+y= The graph of the solution set of the system of inequalities x + y 6, x y, and y is a. b. c. d. x+y=6 x=y x+y=6 x+y=6 x+y=6 x=y x=y x=y Which system of equations has no solution: a. x + y = 9 b. x + y = 9 x + y = 7 x + 8y = 6 c. x + y = 9 d. x - y = 9 x - y = 7 x + y = 9 e. All of the systems have solutions. The maximum value of C = x + y subject to the constraints x + y > 6, x, and y is a. b. c. d.. The minimum value of P = x - y subject to the constraints x - y, x + y, x, and y is a. b. c. - d. -

11 . Two machines produce the same items. Machine A can produce items per hour and machine B can produce items per hour. At least of the items must be produced each -hour week, but the machines cannot be operated at the same time. If it costs $ per hour to operate A and $ per hour to operate B, find the number of hours per week machines A and B, respectively, should be operated to minimize the cost. a. and b. and c. and d. and 6. The graph of y = - (x + ) - is: a. b. c. d. 7. The coordinates of the vertex of y = x + x + are: a. (-, ) b. (-, -) c. (, -) d. (-, -) 8. The graphs of f(x) = x and g(x) = are, respectively, () () () () x a. () and ()b. () and ()c. () and () d. () and ()

12 9. The graphs of f(x) = e x and g(x) = ln x are, respectively, () () () () a. () and ()b. () and ()c. () and () d. () and (). How long would it take for P dollars to double if they are invested at %? Hint: A = Pe rt, where P is the principal, r the rate, t the time in years. a. d. ln. ln ln. b. ln c..