Write the equation of the given line in slope-intercept form and match with the correct alternate form. 10. A

Transcription

1 Slope & y-intercept Class Work Identify the slope and y-intercept for each equation 1. y = 3x 4 2. y = 2x 3. y = 7 m = 3 b = 4 m = 2 b = 0 m = 0 b = 7 4. x = 5 5. y = 0 6. y 3 = 4(x + 6) m = undef b = none m = 0 b = 0 m = 4 b = y + 2 = 1 (x + 6) 8. 2x + 3y = x 7y = 14 2 m = 1 2 b = 5 m = 2 3 b = 3 m = 4 7 b = 2 Write the equation of the given line in slope-intercept form and match with the correct alternate form. 10. A y = 5 x + 5 III 7 I. y + 4 = 1 (x 2) B y = 0x + 6 VI II. No Alternate Form (Slope Undefined) 12. C y = 1 x 3 I 2 III. 5x + 7y = 35 IV. y 6 = 3(x 4) 13. D 14. E y = 2 x 2 V 7 y = 3x 6 IV V. 2x 7y = 14 VI. y 6 = 0(x + 2) 15. F x = 8 II 16. Write an equation: Cal C. drives past mile marker 27 at 11am and mile marker 145 at 1pm. y = 59x + 27 Pre-Calc Parent Functions ~1~ NJCTL.org

2 Slope & y-intercept Homework Identify the slope and y-intercept for each equation 17. y = 5x y = 3x 19. y = 2 m = 5 b = 2 m = 3 b = 0 m = 0 b = x = x = y 4 = 2(x 8) m = undef b = none m = undef b = none m = 2 b = y + 3 = 2 (x + 10) 24. 3x + 4y = x 6y = 12 5 m = 2 5 b = 7 m = 3 4 b = 3 m = 1 3 b = 2 Write the equation of the given line. 26. A y = 3 x 4 V B y = 4x + 8 I I. y + 4 = 4(x 3) II. x + 3y = 1 III. y + 6 = 0(x 1) 28. C x = 6 IV IV. No Alternate Form (Slope Undefined) 29. D V. 3x 2y = 8 y = 1 x 1 II 3 VI. 2x 9y = E y = 2 x 2 VI F y = 0x 6 III 32. Write an equation: Cal C. drives past mile marker 45 at 11am and mile marker 225 at 2pm. y = 60x + 45 Pre-Calc Parent Functions ~2~ NJCTL.org

3 Standard Form Class Work Find the x and y intercepts for each equation x + 3y = x + 5y = 10 x: (6, 0) y: (0, 4) x: ( 5 2, 0) y: (0, 2) 35. x 3y = x = 9 x: (10, 0) y: (0, 10 3 ) x: ( 9 4, 0) y: none 37. y = 0 x: infinite y: (0, 0) Standard Form Homework Find the x and y intercepts for each equation x 5y = x + 2y = 14 x: (5, 0) y: (0, 3) x: (2, 0) y: (0, 7) 40. x y = y = 7 x: (9, 0) y: (0, 9) x: none y: (0, 7) 42. x = 0 x: (0, 0) y: infinite Pre-Calc Parent Functions ~3~ NJCTL.org

4 Horizontal and Vertical Lines Class Work Write the equation for the described line 43. vertical through (1,3) 44. horizontal through (1,3) x = 1 y = vertical through (-2, 4) 46. horizontal through (-2, 4) x = 2 y = 4 Horizontal and Vertical Lines Homework Write the equation for the described line 47. vertical through (4,7) 48. horizontal through (8,-10) x = 4 y = vertical through (8, -10) 50. horizontal through (4, 7) x = 8 y = 7 Pre-Calc Parent Functions ~4~ NJCTL.org

5 Parallel and Perpendicular Lines Class Work Write the equation for the described line in slope intercept form 51. Parallel to y = 3x + 4 through (3,1) 52. Perpendicular to y = 3x + 4 through (3,1) y = 3x 8 y = 1 x Parallel to y = 1 x + 6 through (4, 2) 54. Perpendicular to y = 1 x + 6 through (4, 2) 2 2 y = 1 2 x y = 2x Parallel to y = 5 through ( 1, 8) 56. Perpendicular to y = 5 through ( 1, 8) y = 8 x = 1 Parallel and Perpendicular Lines Homework Write the equation for the described line in slope intercept form 57. Parallel to y = 2x + 1 through ( 6,1) 58. Perpendicular to y = 2x + 1 through ( 6,1) y = 2x 11 y = 1 x Parallel to y = 1 x 5 through ( 6,0) 60. Perpendicular to y = 1 x 5 through ( 6,0) 3 3 y = 1 x + 2 y 3 = 3x Parallel to x = 5 through ( 3,7) 62. Perpendicular to x = 5 through ( 3,7) x = 3 y = 7 Pre-Calc Parent Functions ~5~ NJCTL.org

6 Point-Slope Form Class Work Write the equation for the described line in point slope form. 63. Slope of 6 through (5,1) 64. Slope of -2 through ( 4,3) y 1 = 6(x 5) y 3 = 2(x + 4) 65. Slope of 1 through (8,0) 66. Perpendicular to y = 2x + 1 through (1, 6) y 0 = 1(x 8) y + 6 = 1 (x 1) 2 Convert the following equations to slope-intercept form and standard form 67. y 4 = 5(x + 3) 68. y = 2(x 1) 69. y + 7 = 1 (x 10) 5 y = 5x x y = 19 y = 2x + 2 2x + y = 2 y = 1 x 9 5 x 5y = 45 Point-Slope Form Homework Write the equation for the described line in point slope form. 70. Slope of -4 through (4, 2) 71. Slope of 3 through (0, 9) y + 2 = 4(x 4) y + 9 = 3(x 0) 72. Slope of 1 / 4 through (6,0) 73. Perpendicular to y = 1 x + 6 through (5, 2) 2 y 0 = 1 (x 6) y = 2(x 5) Convert the following equations to slope-intercept form and standard form 74. y 3 = 7(x 2) 75. y + 1 = 4(x 7) 76. y + 3 = 1 (x 18) 6 y = 7x 11 7x y = 11 y = 4x x + y = 27 y = 1 6 x 6 x 6y = 36 Pre-Calc Parent Functions ~6~ NJCTL.org

7 Writing Linear Equations Class Work Write an equation based on the given information in slope intercept form. 77. A line through (7, 1) and ( 3,4) 78. A line through (8,2) and (6, 2) y = 1 2 x y = 2x A line perpendicular to y 7 = 1 (x + 2) through ( 1, 8) 2 y = 2x A line parallel to 4x 6y = 10 through (9,7) y = 2 x A function with constant increase passing through (2,3) and (8,9) y = x The cost of a 3.8 mile taxi ride cost $5.50 and the cost of a 4 mile ride costs $5.70 y = 1. 00x A valet parking services charges $45 for 2 hours and $55 for 3 hours y = 10x + 25 Pre-Calc Parent Functions ~7~ NJCTL.org

8 Writing Linear Equations Homework Write an equation based on the given information in slope intercept form. 84. A line through (4,9) and ( 5, 9) 85. A line through ( 8,2) and (8,2) y = 2x + 1 y = 0x A line perpendicular to 4x 6y = 10 through (2,2) y = 3 x A line parallel to y 7 = 1 (x + 2) through (2,2) 2 y = 1 x A function with constant decrease passing through (2,3) and (8, 9) y = 2x The cost of a 3.8 mile taxi ride cost $8.25 and the cost of a 4 mile ride costs $8.75 y = 2. 50x A valet parking services charges $55 for 2 hours and $75 for 4 hours y = 10x + 35 Pre-Calc Parent Functions ~8~ NJCTL.org

9 Absolute Value Functions Class Work Graph each function. For each, state the domain and range. 91. y = x y = 2x D: R R: [0, ) D: R R: [0, ) 93. y = 2x y = 2 x D: R R: [0, ) D: R R: [0, ) 95. y = x y = 2 x + 3 D: R R: [3, ) D: R R: [3, ) 97. y = x y = 1 2 x 3 D: R R: (, 0] D: R R: (, 3] Pre-Calc Parent Functions ~9~ NJCTL.org

10 Absolute Value Functions Homework Graph each function. For each, state the domain and range. 99. y = x y = 3x D: R R: [0, ) D: R R: [0, ) 101. y = 3x y = 2 3 x D: R R: [0, ) D: R R: [0, ) 103. y = x y = 2 3 x 1 D: R R: [ 1, ) D: R R: [ 1, ) 105. y = x y = 1 4 x + 4 D: R R: (, 0] D: R R: (, 4] Pre-Calc Parent Functions ~10~ NJCTL.org

11 Greatest Integer Functions Class Work Graph each function. For each, state the domain and range y = [x 4] 108. y = [2x] D: R R: Z D: R R: Z 109. y = [2x 4] 110. y = 2[x] D: R R: Z D: R R: 2Z 111. y = [x] y = 2[x] + 3 D: R R: Z D: R R: 2Z y = [x 3] 114. y = 1 2 [x] 3 D: R R: Z D: R R: 1 2 Z Pre-Calc Parent Functions ~11~ NJCTL.org

12 Greatest Integer Functions Homework Graph each function. For each, state the domain and range y = [x + 2] 116. y = [3x] D: R R: Z D: R R: Z 117. y = [3x + 2] 118. y = 2 3 [x] D: R R: Z D: R R: 2 3 Z 119. y = [x] y = 2 3 [x] 1 D: R R: Z D: R R: 2 3 Z 121. y = [x + 4] 122. y = 1 4 [x] + 4 D: R R: Z D: R R: 1 4 Z Pre-Calc Parent Functions ~12~ NJCTL.org

13 Identifying Exponential Growth and Decay Class Work State whether the given function exponential growth or decay. Identify the horizontal asymptote and the y-intercept A B Growth HA: y = 0 y int: (0, 1) Decay HA: y = 0 y int: (0, 1) 124. y = 3(4) x 125. y = 1 2 (3)x Growth HA: y = 0 y int: (0, 3) Growth HA: y = 0 y int: (0, 1 2 ) 126. y = ( 1 2 )x y = 2 ( 1 4 )x 7 Decay HA: y = 4 y int: (0, 5) Decay HA: y = 7 y int: (0, 5) 128. y = 100 ( 1 3 )x y = 17(4) x Decay HA: y = 50 y int: (0, 150) Decay HA: y = 0 y int: (0, 17) 130. y = 12 ( 3 4 ) x y = 1 2 (5) x 2 Growth HA: y = 6 y int: (0, 18) Decay HA: y = 2 y int: (0, ) Pre-Calc Parent Functions ~13~ NJCTL.org

14 Identifying Exponential Growth and Decay Homework State whether the given function exponential growth or decay. Identify the horizontal asymptote and the y-intercept A B Decay HA: y = 2 y int: (0, 3) Growth HA: y = 2 y int: (0, 3) 133. y = 3 ( 2 5 )x 134. y = 5(3) x Decay HA: y = 0 y int: (0, 3) Decay HA: y = 0 y int: (0, 5) 135. y = 6 ( 1 2 )x y = 4(25) x 7 Decay HA: y = 4 y int: (0, 10) Growth HA: y = 7 y int: (0, 3) 137. y = 100 ( 1 3 ) x y = 17(4) x Growth HA: y = 50 y int: (0, 150) Growth HA: y = 0 y int: (0, 17) 139. y = 12 ( 3 4 )x y = 2 5 (7)x 1 Decay HA: y = 6 y int: (0, 18) Growth HA: y = 1 y int: (0, 3 5 ) Pre-Calc Parent Functions ~14~ NJCTL.org

15 Graphing Exponentials Class Work Graph each equation y = 3(4) x 142. y = 1 2 (3)x 143. y = ( 1 2 )x y = 2 ( 1 4 )x y = 100 ( 1 3 )x y = 17(4) x 147. y = 12 ( 3 4 ) x + 6 Pre-Calc Parent Functions ~15~ NJCTL.org

16 Graphing Exponentials Homework Graph each equation 148. y = 3 ( 2 5 )x 149. y = 5(3) x 150. y = 6 ( 1 2 )x y = 4(25) x y = 100 ( 1 3 ) x y = 17(4) x 154. y = 12 ( 3 4 )x + 6 Pre-Calc Parent Functions ~16~ NJCTL.org

17 Intro to Logs Class Work Write each of the following in log form = = = 3 3 log 100 = 2 log 2 16 = 4 log 3 27 = 3 Write each of the following in exponential form log = log 6 36 = log = = = = 343 Solve the following equations 161. log 4 64 = x 162. log 2 64 = x x = 3 x = log 3 y = log 6 y = 3 y = 243 y = log b 81 = log b 10 = 1 b = 3 b = log 5 (x 2) = log 5 (2x 8) 168. log 4 (2x + 7) = log 4 (4x 9) x = 6 x = 8 Pre-Calc Parent Functions ~17~ NJCTL.org

18 Intro to Logs Homework Write each of the following in log form = = = 3 4 log 9 81 = 2 log 2 32 = 5 log 3 81 = 4 Write each of the following in exponential form log 8 64 = log = log 3 81 = = = = 81 Solve the following equations 175. log = x 176. log = x x = 5 x = log 5 y = log 7 y = 4 y = 625 y = log b 1000 = log b 1024 = 10 b = 10 b = log 5 (x + 2) = log 5 (3x 8) 182. log 4 (3x 6) = log 4 (x + 10) x = 5 x = 8 Pre-Calc Parent Functions ~18~ NJCTL.org

19 Properties of Logs Class Work Using Properties of Logs, fully expand each expression 183. log 4 xy 3 z log 6 w x 2 y log 4 x + 3 log 4 y + 4 log 4 z 185. log 7 7m 2 (uv) log 7 m 2(log 7 u + log 7 v) log 6 w 2 log 6 x log 6 y Using log and log , evaluate the following 186. log log log Using Properties of Logs, rewrite the expression as a single log log x + log y log z log 5 m log k 3(log r + log t) log xy z log 5 5 m 3 log k5 (rt) 3 Solve the following equations 192. log 3 x + log 3 4 = log 2 x + log 2 (x + 3) = 2 x = x = log 3 x log 3 4 = 1 4 log log 3 x + log 3 (x 2) = log 3 35 x = 1 x = log 3 x log 3 4 = log log 3 (x + 3) + log 3 (x 2) = log 3 66 x = 8 x = 8 Pre-Calc Parent Functions ~19~ NJCTL.org

20 Properties of Logs Home Work Using Properties of Logs, fully expand each expression 198. log 3 3xy 2 z 5 4w 199. log 4 x log 8 (u 2 v) log 3 x + 2 log 3 y + 5 log 3 z log 8 m 3(2 log 8 u + log 8 v) 1 + log 4 w 2 log 4 x Using log and log , evaluate the following log log log m 4 Using Properties of Logs, rewrite the expression as a single log log x + 3 log y 4 log z log 4 m log f 2 log g 6 log h log x2 y 3 z 4 log 4 4 m 2 log f5 g 2 h 6 Solve the following equations 207. log 3 4x + log 3 2 = log 2 x + log 2 (x 3) = 2 x = x = log 3 x log 3 4 = log log 3 x 2 + log 3 x = log 3 27 x = 64 x = log 3 x log 3 9 = log log 3 (2x + 3) + log 3 (x 2) = log 3 72 x = 15 x = 6. 5 Pre-Calc Parent Functions ~20~ NJCTL.org

21 Common Logs Class Work Solve for the variable x = x+4 = 27 x b 2 = 8 x = log x = 2 log 8 b = log 7 log d 3 = n 2 = 3 n t+2 = 5 t 2 d = log 29 log n = 2 log 7 log 7 log log 5+2 log 4 t = log 5 log 4 Find the approximate value for each 219. log log log Common Logs Home Work Solve for the variable x = x 1 = 4 2x b 6 = 42 x = log x = 8 log 42 b = log 8 log d 1 = n = 7 n t+1 = 32 t 1 d = log 40 log n = 5 log 2 log 7+log log 32+log 18 t = log 32 log 18 Find the approximate value for each 228. log log log Pre-Calc Parent Functions ~21~ NJCTL.org

22 e and ln Class Work Solve the following equations 231. e ln x = e ln x 4 = ln e x+5 = 6x x = 6 x = 10 x = ln e 2x 8 = e 2x = e (x 1) + 9 = 10 x = 2 x = ln x = ln ln(x + 1) = ln(x) + 1 = 7 x = e x = e e and ln Homework Solve the following equations 239. e ln 2x = e ln x 4 = ln e 2x 5 = 6 + x x = 3 x = 2 x = ln e 3x + 9 = e 3x+1 = e (2x+1) + 8 = 10 x = 1 x = ln x = ln ln(x 1) = ln(x) 1 = 9 x = e x = e Pre-Calc Parent Functions ~22~ NJCTL.org

23 Growth and Decay Class Work Solve the following problems 247. $250 is deposited in an account earning 5% that compounds quarterly, what is the balance in the account after 3 years? $ A bacteria colony is growing at a continuous rate of 3% per day. If there were 5 grams to start, what is the mass of the colony in 10 days? grams 249. A bacteria colony is growing at a continuous rate of 4% per day. How long till the colony doubles in size? days 250. If a car depreciates at an annual rate of 12% and you paid $30,000 for it, how much is it worth in 5 years? $15, An unknown isotope is measured to have 250 grams on day 1 and 175 grams on day 30. At what rate is the isotope decaying? At what point will there be 100 grams left? r = = 1. 2% days 252. An antique watch made in 1752 was worth $180 in 1950; in 2000 it was worth $2200. If the watch s value is appreciating continuously, what would its value be in 2010? $3, A furniture store sells a $3000 living room and doesn t require payment for 2 years. If interest is charged at a 5% daily rate and no money is paid early, how much money is repaid at the end? $3, Pre-Calc Parent Functions ~23~ NJCTL.org

24 Growth and Decay Homework Solve the following problems 254. $50 is deposited in an account that earns 4% compounds monthly, what is the balance in the account after 4 years? $ A bacteria colony is growing at a continuous rate of 5% per day. If there were 7 grams to start, what is the mass of the colony in 20 days? grams 256. A bacteria colony is growing at a continuous rate of 6% per day. How long till the colony doubles in size? days 257. If a car depreciates at an annual rate of 10% and you paid $20,000 for it, how much is it worth in 4 years? $13, An unknown isotope is measured to have 200 grams on day 1 and 150 grams on day 30. At what rate is the isotope decaying? At what point will there be 50 grams left? r = = 0. 96% days 259. An antique watch made in 1752 was worth $280 in 1940; in 2000 it was worth $3200. If the watch s value is appreciating continuously, what would its value be in 2010? $4, A $9000 credit card bill isn t paid one month, the credit company charges.5% continuously on unpaid amounts. How much is owed 30 days later? (assume no other charges are made) $10, Pre-Calc Parent Functions ~24~ NJCTL.org

25 Logistic Growth Class Work Scientists measure a wolf population growing at a rate of 3% annually. They calculate the carrying capacity of the region to be 100 members Write a logistic equation to model this situation. P t+1 = P t P t (1 P t 100 ) 262. Create a table that shows the pack population over the next 10 years if P 1= Draw a graph of the equation Logistic Growth Homework A calculus class determines that a rumor spreads around the school at a rate of 15% per hour. The school population is Write a logistic equation to model this situation. P t+1 = P t P t (1 P t 1600 ) 265. Create a table that shows the number of people who know the rumor over the next 10 hours if the class that starts it has 20 members 266. Draw a graph of the equation Pre-Calc Parent Functions ~25~ NJCTL.org

26 Trig Functions Class Work Use the appropriate triangle to answer questions sin θ = 268. cos θ = tan θ = 270. sin α = cos α = 272. tan α = θ = 274. α = A right triangle has a hypotenuse of 7 and an angle of 40, find the larger leg A right triangle has legs of 6 and 10 find the smaller acute angle A right triangle has an angle of 50 and a longer leg of 8, find the hypotenuse Pre-Calc Parent Functions ~26~ NJCTL.org

27 Trig Functions Homework Use the appropriate triangle to answer questions sin θ = 279. cos θ = tan θ = 281. sin α = cos α = 283. tan α = θ = 285. α = A right triangle has a hypotenuse of 9 and an angle of 60, find the larger leg A right triangle has legs of 7 and 12 find the smaller acute angle A right triangle has an angle of 20 and a longer leg of 5, find the hypotenuse Pre-Calc Parent Functions ~27~ NJCTL.org

28 Converting Degrees and Radians Class work Convert the following degree measures to radians and radian measures to degrees π π 36 5π π π π π π π 2 Converting Degrees and Radians Class work Convert the following degree measures to radians and radian measures to degrees π π 12 10π π π π π π 18 35π Pre-Calc Parent Functions ~28~ NJCTL.org

29 Graphing Sin, Cos, and Tan Class Work 305. What is the relationship between when a sine max/min value occurs and when a cosine zero occurs? A sine max/min occurs at the exact same x-value as cosine zeros How do the zeros of the cosine and sine graphs relate to a tangent graph? The sine zeros are where tangent also has zeros. The cosine zeros are where tangent has vertical asymptotes. Consider the domain of ( π, π) for sin θ, cos θ, and tan θ 307. Which function(s) is increasing on the entire interval? tan x 308. Which function(s) has a relative max? sin x, cos x 309. Which function(s) has a concave down interval followed by a concave up interval? cos x, tan x 310. Which function(s) has an undefined value of x on the interval? tan x Graphing Sin, Cos, and Tan Homework 311. What is the relationship between when a cosine max/min value occurs and when a sine zero occurs? 312. How does the tangent function s concavity change between asymptotes? Consider the domain of ( π, π) for sin θ, cos θ, and tan θ 313. Which function(s) is decreasing on the entire interval? 314. Which function(s) has a zero? A cosine max/min occurs at the exact same x-value as sine zeros. Tangent is concave down, then changes to concave up between the vertical asymptotes. none sin x, cos x, tan x 315. Which function(s) has a concave up interval followed by a concave down interval? sin x, tan x 316. Which function(s) has a relative minimum? sin x, cos x Pre-Calc Parent Functions ~29~ NJCTL.org

30 Positive and Negative Integer Power Functions Class Work For each equation find lim x, lim f(x), lim f(x), and lim x 0 x 0 + x 317. f(x) = 4x f(x) = 5x 6 lim f(x) = x x 0 x 0 + lim f(x) = x lim f(x) = x x 0 x 0 + lim f(x) = x 319. f(x) = 1 3 x f(x) = x 2 lim f(x) = x x 0 x 0 + lim x f(x) = lim f(x) = x x 0 x 0 + lim x f(x) = 321. f(x) = 4x f(x) = 5x 6 x lim f(x) = x 0 lim f(x) = x 0 + x x lim f(x) = x 0 lim f(x) = x 0 + x 323. f(x) = 1 3 x f(x) = x 2 x lim f(x) = x 0 lim f(x) = x 0 + x x lim f(x) = x 0 lim x 0 + f(x) = lim x f(x) = 0 Pre-Calc Parent Functions ~30~ NJCTL.org

31 Positive and Negative Integer Power Functions Homework For each equation find lim x lim f(x), lim f(x), and lim x 0 x 0 + x 325. f(x) = 3x f(x) = 2x 8 lim f(x) = x x 0 x 0 + lim f(x) = x lim f(x) = x x 0 x 0 + lim x f(x) = 327. f(x) = 1 4 x f(x) = 6x 20 lim f(x) = x x 0 x 0 + lim x f(x) = lim f(x) = x x 0 x 0 + lim f(x) = x 329. f(x) = 3x f(x) = 2x 8 x lim f(x) = x 0 lim f(x) = x 0 + x x lim f(x) = x 0 lim f(x) = x 0 + x 331. f(x) = 1 4 x f(x) = 6x 20 x lim f(x) = x 0 lim f(x) = x 0 + x lim x f(x) = 0 lim x 0 f(x) = lim x 0 + f(x) = lim x f(x) = 0 Pre-Calc Parent Functions ~31~ NJCTL.org

32 Rational Power Functions Class Work Choose which function(s) fits the description provided. (A) f(x) = x (B) f(x) = x (C) f(x) = x (D) f(x) = x 333. undefined for negative real values 334. lim f(x) = x B and C A and D 335. closest to (10,1) 336. lim x 0 + f(x) = 0 D A, B, C, and D 337. lim f(x) = undefined 338. closest to (10, 3) x 0 B and C A Rational Power Functions Homework Choose which function(s) fits the description provided. (A) f(x) = x (B) f(x) = x (C) f(x) = x (D) f(x) = x 339. Domain is (, ) 340. lim x f(x) = A and D None 341. closest to (5,-1.5) 342. lim x 0 f(x) = undefined B B and C 343. Range is (, 0] 344. closest to (10,- 1.5) Pre-Calc Parent Functions ~32~ NJCTL.org

33 B and C C Rational Functions Class Work For each of the following functions, name any discontinuities and tell whether they are non-removable or removable. Graph each function h(x) = 3x2 4x 4 x g(x) = x 5 x 2 25 x = 2 removable x = 2 non-removable x = 5 removable x = 5 non-removable 347. j(x) = x2 12x+36 x m(x) = x 2 9 x 2 6x+9 x = 6 removable x = 3 non-removable clipboard(67).galleryitem 349. lim f(x) = lim f(x) = 2; f(3) is undefined x 3 + x 3 x = 3 removable Graphs will vary. Any graph that would go through the point (3,2), but instead has a hole at that point. Pre-Calc Parent Functions ~33~ NJCTL.org

34 Rational Functions Homework For each of the following functions, name any discontinuities and tell whether they are non-removable or removable. Graph each function h(x) = x2 4x+4 x g(x) = x 4 x 2 16 x = 2 removable x = 2 non-removable x = 4 removable x = 4 non-removable 352. j(x) = 2x2 8x 24 x 6 x = 6 removable 353. m(x) = x 2 49 x 2 +14x+49 x = 7 non-removable 354. lim x 5 f(x) = lim f(x) = 1; f( 5) is undefined x 5 + x = 5 removable Graphs will vary. Any graph that would go through the point ( 5,1), but instead has a hole at that point. Pre-Calc Parent Functions ~34~ NJCTL.org

35 Unit Review - Multiple Choice 1. Which equation has an x-intercept of (5,0) and a y-intercept of (0, 5 2 ) a. y + 5 = 5(x 0) 2 b. y 5 = 5(x 0) 2 C c. y = 1 (x 5) 2 d. y = 1 (x + 5) 2 2. The equation of a line perpendicular to 2x + 3y = 7 and containing (5,6) is a. 3x 2y = 3 b. y 6 = 2 (x 5) 3 c. 3x 2y = 4 d. y = 2 (x 6) 3 3. A line with no slope and containing (3,8) has equation a. y = 3 b. y = 8 B c. x = 3 d. x = 8 4. The vertex of y = 2 x is a. (2,7) b. ( 2,7) c. ( 1,7) D d. (1,7) 5. 4[ 3(2.7) + 0.5] = a. 40 b. 36 c. 32 C d The equation that models exponential decay passing through (0,5) and a lim f(x) = 4 is x a. f(x) = 5e x + 4 b. f(x) = 1e x + 4 D c. f(x) = 5e x + 4 d. f(x) = 1e x A forest fire spreads continuously, burning 10% more acres every hour. How long will it take for 1000 acres to be on fire after 200 acres are burning? a hours b hours B c hours A Pre-Calc Parent Functions ~35~ NJCTL.org

36 d. not enough information 8. log 6 5 = a..116 b..898 c d Given 4 x = 10, find x a. 2.5 b..602 c..400 d log m =.345 and log n = 1.223, find log 10m2 n 3 a b..651 A c d Which of the following would not influence the carrying capacity of a logistic growth model a. the population of a town b. the food supply in an ecological preserve c. the rate of spread of the flu C d. the area inside a Petri dish 12. The larger leg of a right triangle is 6 and the smallest angle is 20, what is the hypotenuse? a b A c d How many degrees is 4π 9? a. 160 b. 110 C c. 80 d An example of a function that is concave down and then concave up is a. f(x) = sin x on (0, π) b. f(x) = tan x on (0, π) c. f(x) = cos x on (0, π) C d. f(x) = sin x on ( π, π) 15. The function that has lim f(x) = and lim x 0 a. f(x) = 3x 3 B D f(x) = is x 0 + Pre-Calc Parent Functions ~36~ NJCTL.org

37 b. f(x) = 4x 4 c. f(x) = 3x 3 d. f(x) = 4x 4 C 16. The function h(x) = 4x2 3x 1 4x 2 1 has the following discontinuities a. non-removable discontinuity at x = ± 1 2 b. removable discontinuity at x = ± 1 2 A c. non-removable discontinuity at x = 1 2 ; removable discontinuity at x = 1 2 d. non-removable discontinuity at x = 1 2 ; removable discontinuity at x = 1 2 Extended Response 1. Consider the function h(x) = f(x) g(x), if f(x) = x2 2x 8 and g(x) = x 2 + 8x + 15 a. Use limit notation to describe the end behavior of h(x) lim h(x) = +1 x h(x) = +1 lim x b. Name any discontinuities and whether they are removable or non-removable. x = 5, 3 both non removable c. j(x) = h(x) m(x) and has a removable discontinuity at x = 3,what is m(x)? m(x) is any polynomial with x + 3 as a factor, or any rational function with x + 3 as a factor of the numerator 2. Entomologists introduce 20 of one variety of insect to a region and determine that the population doubles every 6 hours. a. Write an equation to model this situation. A = 20e t b. What will the population be in 10 hours? hours Pre-Calc Parent Functions ~37~ NJCTL.org

38 c. If those same scientists determine that the region can support a maximum of 100,000 of the species, rewrite your equation from part a. P t+1 = P t P t (1 3. A compostable bag breaks down such that only 10% remains ) in 6 months. a. If the decomposition is continual, at what rate is the bag decomposing? P t r = 38.4% decay per month b. How much of the bag remained after 4 months? 21.5% remaining c. When will there be less than 1% of the bag remaining? after 12 months 4. A 15 ladder is rated to have no more than a 70 angle and no less than a 40 angle. a. What is maximum rated distance the ladder can be placed from the wall? 11.5 feet b. How high up a wall can the ladder reach and be within the acceptable use limits? 14.1 feet c. At what base angle should the ladder be placed to reach 10 up the wall? 41.8 Pre-Calc Parent Functions ~38~ NJCTL.org