49) f (x) = 1 2 (x + 2)2 + 4

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1 Algebra i FI0zp` skauetyan usxogfjtuwaxr`e_ `LsLFCL.W V earlnlz DrGi]grhYtbsd srenspe[roveeed. EOC Stud Guide Identif the verte, ais of smmetr, direction of opening, min/ma value, -intercept, and -intercepts of each. Name Describe the transformation of f () from g() = Period ) f () = ( - 3) - 5 9) f () ( + ) + Find the inverse of each function. 50) g() = - 3 5) g() = ) = ) = log ( + ) Use the information provided to write the verte form equation of each parabola. Then find he verte. 5) f () = ) f () = + + Divide. 5) ( ) ( - 0) 57) ( ) ( - ) Evaluate each epression. 59) log 5) log Use a calculator to approimate each to the nearest thousandth. 0) log 5 ) log 7 7 Condense each epression to a single logarithm. ) log log 5 3) log - log Epand each logarithm. ) log ( c a) 5) log 7 ( z 5 ) Worksheet b Kuta Software LLC

2 Identif the domain and range of each. Then sketch the graph. ) f () = log ( - ) + 7) f () = log ( - ) Solve each equation. ) log 5 - log 5 ( - ) 9) log log 5 5 Solve each equation. Round our answers to the nearest ten-thousandth. 70) -5e - 0 = -.7 7) e ) Find the time required for an investment of $000 to double if the interest rate of 9.5% is compounded continuousl. Find the eact value of all si trigonometric functions. 7) q = 7p 73) The needle of the scale in the bulk food section of a supermarket is 5 cm long. Find the distance the tip of the needle travels when it rotates 9. 75) An angle whose endpoint lies at (3, -) 7) simplif: cos sin - cos 77) simplif: tan - tan sin 7) tan (sec - ) Evaluate each arithmetic series described. 0) Sk 79) - sec tan 5 (0k - 5) ) Sk - (k - 7) tan - sec ) To find the height of a pole, a surveor moves 00 feet awa from the base of the pole and then, from an ee-level height of 5.5 feet, measures the angle of elevation to the top of the pole to be 7. Find the height of the pole to the nearest foot. 3) A 0-foot ladder makes an angle of 5 with the ground as it leans against a barn. How far up the barn does the ladder reach? Worksheet b Kuta Software LLC

3 Sketch the graph of each function. ) f () ( + ) 5) f () = Solve each triangle. Round answers to the nearest tenth. ) B 7) C C 5 A ) A pole 50 feet tall is situated at the bottom of a hill that slopes up at an angle of.9. A gu wire from the top of the pole to the hillside forms an angle of 37 with the top of the pole. Find the distance from the base of the pole to the gu wire s point of attachment. A 5 7. B 9) A group of 0 people attend a ball game. There were four times as man children as adults in the group. Set up a sstem of equations that represents the numbers of adults and children that attended the game and solve the sstem to find the number of children that were in the group. Given the first term and the common difference of an arithmetic sequence find the term named in the problem, the eplicit formula, and the recursive formula. 90) a = -, d = 9 Find a 9) a = -35, d = -0 Find a 9 Evaluate each arithmetic series described. 9) a, a n =, n = 7 93) a 9, d =, n = 0 9) , n 95) , n Worksheet b Kuta Software LLC

4 Evaluate each geometric series described. 9) Sk - k - 97) a = -, a n, r = - Find the common ratio, the th term, the eplicit formula, and the recursive formula. 9) 3, 5, 75, 375,... 99) In 9, the average cost of a ticket on a privatel-owned airline was $0. This amount has increased b approimatel $55 earl. How much should ou epect to pa for a ticket on this airline in the ear 003? 00) A woman made $0,000 during the first ear of her new job at cit hall. Each ear she received a 0% raise. Find her total earnings during the first seven ears on the job. Solve each equation for 0 q < 30. 0) 3 + tan q = 0) 0 = tan q Solve each equation for 0 q < p. 03) 3 = -cos q 0) - + tan q = - 05) State all three pthagorean identies 0) State all reciprocal identities. Sketch two ccles of the graph of the functions. 07) Sketch two ccles of the graph of the function = 3cos q - 0) = - + sin q Worksheet b Kuta Software LLC

5 Algebra H UY0\uf ]KXuktHac FSgofktcwJasr[eM ILDLgCc. GAvllJ Zrcilg`hGtBs` OrCeCsNegrdvfe_d^. EOC Stud Guide Identif the verte, ais of smmetr, direction of opening, min/ma value, -intercept, and -intercepts of each. ) f () = ( - 3) - 5 Verte: (3, -5) Ais of Sm.: = 3 Opens: Up Min value = -5 -int: - -int: and - Find the inverse of each function. Name Describe the transformation of f () from g() = 9) f () ( + ) + vertical compression b shift to the left and up 50) g() = - 3 g - () = -( - ) 3 5) g() = () g- = 3-5 5) = - 0 = log ( + 0) 53) = log ( + ) = - Use the information provided to write the verte form equation of each parabola. Then find he verte. Period 5) f () = f () = -( - ) - 7 Divide. (, -7) 5) ( ) ( - 0) Evaluate each epression. 55) f () = + + f () = ( + ) + (-, ) 57) ( ) ( - ) ) log - 59) log 3 Use a calculator to approimate each to the nearest thousandth. 0) log 5. ) log Condense each epression to a single logarithm. ) log log 5 log 5 ( 3 ) 3) log - log log Epand each logarithm. ) log ( c a) log c + log a 5) log 7 ( z 5 ) log 7 + log log 7 z Worksheet b Kuta Software LLC

6 Identif the domain and range of each. Then sketch the graph. ) f () = log ( - ) + Domain: > Range: All reals 7) f () = log ( - ) - Domain: > Range: All reals Solve each equation. ) log 5 - log 5 ( - ) { 5 } 9) log log 5 5 { 3, - 3 } Solve each equation. Round our answers to the nearest ten-thousandth. 70) -5e - 0 = ) e ) Find the time required for an investment of $000 to double if the interest rate of 9.5% is compounded continuousl. Find the eact value of all si trigonometric functions. 7) q = 7p sin q = -, csc q = ears 73) The needle of the scale in the bulk food section of a supermarket is 5 cm long. Find the distance the tip of the needle travels when it rotates 9. 75) An angle whose endpoint lies at (3, -) 0. cm 3 cos q = -, sec q = tan q = 3, cot q = 3 sin q = - 5, csc q = - 5 cos q = 3 5, sec q = 5 3 tan q = - 3, cot q = - 3 7) simplif: cos sin - cos -cos 77) simplif: tan - tan sin sin 7) tan (sec - ) tan Evaluate each arithmetic series described. 79) - sec tan - tan - sec cot 0) Sk 5 (0k - 5) 05 ) Sk (k - 7) 0 ) To find the height of a pole, a surveor moves 00 feet awa from the base of the pole and then, from an ee-level height of 5.5 feet, measures the angle of elevation to the top of the pole to be 7. Find the height of the pole to the nearest foot. 3 ft. 3) A 0-foot ladder makes an angle of 5 with the ground as it leans against a barn. How far up the barn does the ladder reach? 5.7 ft Worksheet b Kuta Software LLC

7 Sketch the graph of each function. ) f () ( + ) 5) f () = Solve each triangle. Round answers to the nearest tenth. ) B 7) C 3.9 C A ) A pole 50 feet tall is situated at the bottom of a hill that slopes up at an angle of.9. A gu wire from the top of the pole to the hillside forms an angle of 37 with the top of the pole. Find the distance from the base of the pole to the gu wire s point of attachment. 3. ft A B 9) A group of 0 people attend a ball game. There were four times as man children as adults in the group. Set up a sstem of equations that represents the numbers of adults and children that attended the game and solve the sstem to find the number of children that were in the group. children Given the first term and the common difference of an arithmetic sequence find the term named in the problem, the eplicit formula, and the recursive formula. 90) a = -, d = 9 Find a a = 03 Eplicit: a n = n Recursive: a n = a n a = - Evaluate each arithmetic series described. 9) a = -35, d = -0 Find a 9 a 9 = -35 Eplicit: a n = -5-0n Recursive: a n = a n a = -35 9) a, a n =, n = ) a 9, d =, n = ) , n 53 95) , n 00 Worksheet b Kuta Software LLC

8 Evaluate each geometric series described. 9) Sk - k ) a = -, a n, r = - 5 Find the common ratio, the th term, the eplicit formula, and the recursive formula. 9) 3, 5, 75, 375,... Common Ratio: r = 5 a = 3375 Eplicit: a n = 3 5 n - Recursive: a n = a n - 5 a = 3 00) A woman made $0,000 during the first ear of her new job at cit hall. Each ear she received a 0% raise. Find her total earnings during the first seven ears on the job. $9,73. 99) In 9, the average cost of a ticket on a privatel-owned airline was $0. This amount has increased b approimatel $55 earl. How much should ou epect to pa for a ticket on this airline in the ear 003? $935 Solve each equation for 0 q < 30. 0) 3 + tan q = {35, 35} 0) 0 = tan q {0, 0} Solve each equation for 0 q < p. 03) 3 = -cos q { 5p, 7p } 0) - + tan q = - {0, p} 05) State all three pthagorean identies sin + cos sec = tan + csc = cot + Sketch two ccles of the graph of the functions. 0) State all reciprocal identities. sin q = csc q cos q = sec q tan q = cot q 07) Sketch two ccles of the graph of the function = 3cos q - 0) = - + sin q - p - p p 3p p 5p 3p 7p p - p - p p 3p p 5p 3p 7p p - - Worksheet b Kuta Software LLC

2. Find the value of y for which the line through A and B has the given slope m: A(-2, 3), B(4, y), 2 3

2. Find the value of y for which the line through A and B has the given slope m: A(-2, 3), B(4, y), 2 3 . Find an equation for the line that contains the points (, -) and (6, 9).. Find the value of y for which the line through A and B has the given slope m: A(-, ), B(4, y), m.. Find an equation for the line