x x 5, x no real solutions. x a. 103 feet. b seconds

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1 BRIDGE TO ALGEBRA B ,. 5, 3. no real solutions a. 03 feet b. 5.3 seconds 6. a. There are two times when the ball is si feet above the ground. The first is immediately after the ball is kicked, and occurs at seconds. The second is farther downfield and while the ball is heading back toward ground; this occurs at seconds. b. 4.7 seconds c or feet MCPS 0 0

2 BRIDGE TO ALGEBRA B / / Interval notation is used in the chart below, but inequality notation is acceptable as are precise words such as All real numbers greater than or equal to 3. Domain Range Ais of Symmetry Verte min. or ma. Transformation(s) from f I, 3, 5 5,3 min. Right 5 units Up 3 units II,, 4 6 6, 4 ma. Reflect over -ais Left 6 units Down 4 units III,,6 IV, 5,,6 ma. Reflect over -ais Left units Up 6 units 4 4, 5 min. Right 4 units Down 5 units Equation f 5 3 f 6 4 f ( ) ( ) 6 f ( ) ( 4) 5 9. D MCPS 0 0

3 BRIDGE TO ALGEBRA B 0. a. Right units and down 4 units b., 4 c. y d. 0 and 4. Can also be written as 0,0 and 4,0. e. 0. Can also be written as 0,0.. a. Dilation, or vertical stretch, by a factor of 5. b. Dilation, or vertical shrink, by a factor of, then up 3 units. c. Reflection over -ais and dilation, or vertical stretch, by a factor of.. a. y b. 50 miles per hour c. The verte is 3.5, At time period 3.5, which corresponds to 5:5 P.M., the average speed is miles per hour. Because this verte is a minimum, it indicates the time at which the average speed is the slowest. MCPS 0 0 3

4 BRIDGE TO ALGEBRA B 3. a. y b. $440. Eplanations: y 0(4) 40(4) 00 I replaced with 4.00 in the function and obtained 440. c. $445. Eplanations: The verte of the parabola gives the maimum value for the revenue. The verte (found by graphing) is at 3.5,445. The verte of the parabola gives the maimum value for the revenue and b 40 is on the ais of symmetry. The ais of symmetry is 3.5 a 40 So, the value of the verte is 3.5 Substituting 3.5 for into the equation I determined in part a gives the maimum value of y which is 445. d. $3.00 Justifications: The amount of revenue when the price is reduced by $3.00 is $440. The amount of revenue when the price is reduced by $5.00 is $400. Therefore, more revenue is obtained when the price is reduced by $3.00 rather than $5.00. y 0(3) 40(3) 00 y 440 y 0(5) 40(5) 00 y 400 I looked on the graph and saw that $3.00 is closer to the ais of symmetry, which contains the maimum, than $5.00, so the y-value is higher when is $3.00 than when is $5.00. MCPS 0 0 4

5 BRIDGE TO ALGEBRA B 4. a. b. y 7 c. eponential growth d. all real numbers e. No. Sample justification: There is an asymptote at y 7. Since the graph will never touch the asymptote, f will never be f f B 8. a. dilation or vertical stretch by a factor of 3 b. horizontal asymptote, growth factor, domain, range 9. a. vertical translation up 7 units b. growth factor, domain 30. eponential growth 3. eponential decay 3. eponential growth 33. eponential decay MCPS 0 0 5

6 BRIDGE TO ALGEBRA B 34. a. Number of Months after Purchase, m Value of Gift Card, v b. v m 35. a. y b = 064 or 065 boats c Justifications: I graphed the equations y and y 500 into my calculator and determined that the -value of the point of intersection was between 7 and and The value of is a whole number: so, The 500 th boat will visit the harbor during 008. I tried different values of and found that when 7, y 500, but when 8, y 500. So, the 500 th boat visits the harbor when is So, the 500 th boat will visit the harbor during 008. d. Approimately 8 % per year. 36. Colony I: y.5 Colony II: y Colony I: The number of bacteria is doubling every day. Colony II: The number of bacteria is halving every day. 38. On day 39. C MCPS 0 0 6

7 BRIDGE TO ALGEBRA B 40. B 4. a. $600 b. Yes or No depending on justification. No because the -ais is an asymptote and so the y-value will never mathematically be zero. Yes because eventually the value will be less than $.0 which is economically equivalent to 0. c. 3. The value of the boat decreases by 3% each year. 4.. / / a. k 3,000 sp k 8(4000) k k 3,000 b. The total number of square feet in the park that will be available to those who attend the concert. c. 3, 000 s sp 3,000 p d. 3. MCPS 0 0 7

8 BRIDGE TO ALGEBRA B 44. a. k 7 D ks 3 k() k 7 b. k is the ratio of the depth of the water to the distance from shore. Every foot farther into the water corresponds to an increase in water depth of 7 of a foot. c. 8 feet D ks 4 7 s s 8 feet d. 5.5 feet D ks D D 5.5 e. D s a. k y k 480 k40 k b. The number of dollars Amon earns each hour c. $6 y k y (8) 6 d. 30 y k e. y MCPS 0 0 8

9 BRIDGE TO ALGEBRA B / / linear 48. linear 49. eponential 50. quadratic 5. eponential 5. eponential MCPS 0 0 9