Chapter 3 Equations and Inequalities in Two Variables and Functions

Transcription

1 Chapter Equations and Inequalities in Two Variables and Functions Exercise Set.. (+,+), (,+), (, ), (+, ).. Replace one of the variables with a chosen number (any number).. Solve the equation for the other variable. 6. At least two solutions must be found to graph the line; however, it is wise to find three solutions, using the third solution as a check. 8. To find an x-intercept:. Replace y with 0 in the given equation.. Solve for x. To find a y-intercept:. Replace x with 0 in the given equation.. Solve for y. 0. A:(, ), B:(, ), C:(5, ), D:(, 0). a. II b. I c. x-axis d. IV 8. Yes 0. No. No. No a. IV b. y-axis c. IV d. II. 6. a.. b. units c. 57 square units

2 Chapter Equations and Inequalities in Two Variables and Functions

3 Instructor s Solutions Manual ( 0, 0 ) 58. ( 6, 0 ) ( 0, ) 68. (, 0) ( 0, ) 60. (, 0 ) ( 0, ) 6. (, 0) ( 0, ) 70. When m is positive, the graph increases from left to right. When m is negative, the graph decreases from left to right. 7. Subtracting b (where b > 0) shifts the graph down the y-axis. 7. a) (, 5) (, 5), (, ), (, ) b) (, ), (, ), (, ), (, ) c) [(x + 5), (y )] 76. a) $70 b) hr. c) 6.,0 ( ) 0,

4 6 Chapter Equations and Inequalities in Two Variables and Functions 78. a) $ b) 8 days c) ; 0, m = ( ) 80. a) $75 b).5 hr. c) ; 0, 5 0. m = ( ). m = ; ( 0, ) Exercise Set.. Plot (0, ), then rise and run to find another point.. If m < 0, then the graph is a line that slants downward from left to right. 6. It is a vertical line because the x-coordinates are the same. 8. y x. m = ; 0, 5 0. y x. downward. upward 6. m ; 0,. m ; 0, b. f. a 6. c 5 ; 0, 6. m = ( )

5 Instructor s Solutions Manual m = ; 0, a) 0. b) Her BMI increases 0. units for every pound of weight she gains. 6. a) m = ; 0,. m = ; ( 0,0) 5 b) or 6.5 c) a) undefined b) c) a) 56. a) b) 0.85 b) ma = ; mb = ; mc = 5 c) They are reciprocals with opposite signs.

6 8 Chapter Equations and Inequalities in Two Variables and Functions 70. a) b) Collaborative Exercises a) m 0 b) It is the ratio of the values shown outside the table. 7. y x 8, 6. (, ) and ( ) Exercise Set.. To write the equation of a line given any two points, x, y and x, y, we calculate the slope y y using m, then use ( y y) m( x x). x x. If necessary, multiply both sides by the LCD and distribute to make the coefficients and constant term integers. Then use the addition property of equality to get the x and y terms on one side of the equation and the constant on the other side. 6. b a 8. y = x 0. y = x+. y =.6x+.5 ;0, y = x+. m ;0, y = x 6. m 8. y = x y = x. y = x. y = x 6. y = x y = x+ 7 y = x 5. y = x+. a) y = x b) x y = 6. a) y = x+ 5 b) x+ y = a) y = x+ b) 5x y = 6 0. a) y = x+ b) x y = 6 9. a) y = x b) x+ y = 9. a) y = x b) x+ y = 6. parallel 8. perpendicular 50. neither 5. parallel 5. perpendicular 56. perpendicular

7 Instructor s Solutions Manual a) y = x b) x+ y = 86. a) 60. a) y = x+ b) x y = 5 6. a) y = x+ b) 5x y = 6. a) y = x+ b) x y = 66. a) y = x b) x y = b) 0. c) p 0.t d) $7.9 in or $ a) 68. a) y = x+ b) x+ y = 70. a) y = x b) x y = a) y = x b) x+ y = 9 7. a) y = x+ b) x y = 76. a) y = x b) x y = 78. x 80. x 0 8. a).6 b) c.6t. c) $ a) 7. b) n = 7.t+ 87 c) 87. million, or 87,00,000 CDs b) 0.5 c) p = 0.5t +.7 d) 8.% Exercise Set.. Replace the inequality with an = symbol.. Choose an ordered pair on one side of the boundary line and test this ordered pair in the inequality. If the ordered pair satisfies the inequality, then shade the region that contains it. If the ordered pair does not satisfy the inequality, then shade the region on the other side of the boundary line. 6. No 8. Yes 0. No. No.

8 0 Chapter Equations and Inequalities in Two Variables and Functions

9 Instructor s Solutions Manual 0. a) x represents the number of large bottles sold and y represents the number small bottles sold. b). a).5x 5.5y 75 b) c) All sales combinations that cause the company to break even ($00,000 revenue). d) All sales combinations that give the company a profit (more than $00,000 revenue). e) Answers may vary. Two examples are (80,000, 0) and (0,000, 00,000). f) Answers may vary. Two examples are (0,000, 00,000) and (0, 50,000). g) No, fractions of bottles cannot be sold.. a) l w 50 b) c) All combinations of length and width that make the perimeter exactly 50 ft. d) All combinations of length and width that make the perimeter less than 50 ft. e) Answers may vary. Two examples are (0, 85) and (60, 65). f) Answers may vary. Two examples are (0, 0) and (5, 0). c) All combinations that cost exactly $75. d) All combinations that cost less than $75. e) Answers may vary. Two examples are (7, ) and (6, ). f) Yes, (, ) and (, 6). Exercise Set.5. The range is a set containing all values that are paired with the domain in a relation; its output values; the second coordinates in ordered pairs.. If each vertical line intersects the graph in at most one point, then the relation is a function. If any vertical line intersects the graph at two or more different points, then the relation is not a function. 6. Yes, its graph will pass the vertical line test. 8. Domain: {New York, Los Angeles, Chicago, Houston, Philadelphia} Range: {8,,6,,89,78,,8,,,,9,,5,986} 0. Domain: {00, 00, 005, 006, 007, 008} Range: {Louisiana State, Southern California, Texas, Florida} It is not a function. Domain: {,,,, 5, 8, 9, 0} Range: {The Closer, Cheetah Girls One World, Law & Order, NASCAR Sprint Cup, Monk, The SpongeBob Squarepants Movie, WWE Entertainment, Saving Grace, Psych, SpongeBob, Burn Notice, NFL Preseason Football} It is not a function. Domain: {,,, } Range: {Iron Man, What Happens in Vegas, Speed Racer, Made of Honor} 6. Domain: {8,,, 5} Range: {, 5, 6, }

10 Chapter Equations and Inequalities in Two Variables and Functions 8. Domain: {,, } Range: {, 5,, } It is not a function 0. Domain: {,,, } Range: {8, }. Domain: {99, 99, 995, 996, 997, 998, 999, 000, 00, 00, 00, 00, 005, 006} Range: {9, 0, 7, 6, 9, 8, 897, 97, 70, 66, 08, 55, 80}. Domain: or (, Range: { yy 0} or [ 0, 6. Domain: { xx 0} or [ 0, Range: or (, It is not a function 8. Domain: { x 5 x 5} or [ 5,5] Range: { y y,, y 5} [,) [, ] (,5] < < or 0. Domain: { x x } or [,] Range: { y 0 y } or [ 0, ]. a) 8 b) c) d) 6t 0. a) b) c) 9 d) a + a 6. a) Not real b) c) 0 d) a 8. a) 0 b) c) d) t 0. a). b) 0. c) 0.5 d).a + a. a) Not real b) c) 0 d) w + 5w. a) b) c) 0 d) 6. a) 7 b) Undefined c) d) 8. a) 7 b) 8 c) Undefined a d) a a) b) Undefined c) Not real a d) a 5 5. a) b) 0 c) 5. a) 8 b) c) 56. a) b) c) 58. Domain: or (, Range: or (,

11 Instructor s Solutions Manual a) 6. Domain: or (, Range: or (, b) $0 70. a) pd 0.85d 00 b) 6. Domain: or (, Range: or (, c) $ a) 66. Domain: or (, Range: { y y < } or [, b) No c) The radius of the cylinder is. cm. d) 6. cubic centimeters 7. a) Domain: or (, Range: { y < y } or (, ] b) yes; 0.6 c) pt 0.6t 5.8 d) $8.6