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1 1 of 39 1/18/017 10:43 AM Student: Date: Instructor: Alfredo Alvarez Course: 017 Spring Math 1314 Assignment: Practice Final 1. Graph the equation. y= x 3 ID: Perform the multiplication and write the expression shown below in standard form. ( 5 6i)( 5+4i) 1+50i 49 10i 1 10i 49+50i ID: Divide and express the result in standard form i i i i ID:

2 of 39 1/18/017 10:43 AM 4. Solve the equation by factoring. x +7x 60= 0 { 15, } { 1, 5} { 1, 5} { 1,1} ID: Solve for the variable x in the equation shown below. 16x + 3x + 15 = 0 3 4, , , , 1 3 ID: Solve the equation by the square root property. (4x + ) = 36 {,1} {1, } { 1010, } {0,1} ID: Solve the equation by completing the square. x + 1x + 7 = 0 { 0 1, } { 6±36i} { 6±6i} { 6+6i} ID:

3 3 of 39 1/18/017 10:43 AM 8. Solve the equation using the quadratic formula. x +4x 96=0 { 1,1} { 81, } { 1, 8} { 18, } ID: Solve the equation using the quadratic formula. 7x + 8x + = 0 4 7, , , 4+ 14, 8+ 7 ID: Solve the equation using the quadratic formula. x + 1x + 5 = 0 { 6 4i, 6+4i} { 6+4i} { 10, } { 6 16i, 6+16i} ID: 1.5-6

4 4 of 39 1/18/017 10:43 AM 11. Solve the equation by the method of your choice. 9x 71x 8=0 1 9,8 { 98, } 1 9,9 1 9, 1 71 ID: Solve the equation by the method of your choice. 6x = 1x , , 6, , ID: Solve the equation by the method of your choice. x + 14x + 38 = 0 { 7 38, } { } { 7 11, } { } ID:

5 5 of 39 1/18/017 10:43 AM 14. Solve the polynomial equation by factoring and then using the zero product principle. 3 x +4x x 4=0 { 1,1, 4} { 44, } {1, 44, } { 16} ID: Solve the radical equation, and check all proposed solutions. x+1 = { 9} { 4} { 3} { 5} ID: Solve the radical equation, and check all proposed solutions. 5x 4 =x+6 { 8} { 5} { 8, 5} ID: Solve the radical equation, and check all proposed solutions. x 3x = 4 {1,} { 1} {9} {,9} ID: 1.6-9

6 6 of 39 1/18/017 10:43 AM 18. Solve the absolute value equation or indicate that the equation has no solution. 4x =15 1 4, 17 4 { 17 1, } , 1 4 ID: Solve the absolute value inequality using an equivalent compound inequality. Other than express the solution set and graph the solution set on a number line. x 5 < 7, use interval notation to [ 1, ] (, ) ( 1, ) ( 1, ) ID: Solve the absolute value inequality using an equivalent compound inequality. Other than express the solution set and graph the solution set on a number line., use interval notation to 3+ 1 x 5 (, 6] [, ) (, ] [ 6, ) [ 6, ] [ 6, ] ID:

7 7 of 39 1/18/017 10:43 AM 1. Use the graph of the given function to find any relative maxima and relative minima. f(x) = x 3 3x + 1 Maximum: none; minimum: (, 3) Maximum: (0,1); minimum: none Maximum: (0,1); minimum: (, 3) No maximum or minimum ID:.-6. Use the graph of the given function to find any relative maxima and relative minima. f(x) = x 3 1x + Minimum: (, 14) Maximum: (,18) No maxima or minima Maximum: (, 14) Minimum: (,18) Maxima: (,18) and (0,0) Minimum: (, 14) ID:.-7

8 8 of 39 1/18/017 10:43 AM 3. Evaluate the piecewise function at the given value of the independent variable. f(x) = 3x 4 if x < 1 ; f( 1) x + 4 if x and 1 ID: Graph the function. f(x) = x+1 if 9 x< 4 6 if x= 4 x+3 if x> 4 ID: Find and simplify the difference quotient f(x + h) f(x), h 0 h for the given function. f(x) =x +x 8 x + h + x + h 8 1 x +x+xh+h +h 16 h ID:.-19

9 9 of 39 1/18/017 10:43 AM 6. Use the graph of the function f, plotted with a solid line, to sketch the graph of g(x) = f(x ). ID: Begin by graphing the standard square root function f(x) = x. Then use transformations of this graph to graph the given function. h(x) = x+1 ID:.5-6

10 10 of 39 1/18/017 10:43 AM 8. Begin by graphing the standard quadratic function f(x) =x. Then use transformations of this graph to graph the given function. h(x) = (x 5) +3 ID: Begin by graphing the standard absolute value function f(x) = x. Then use transformations of this graph to graph the given function. g(x) = x 3 ID: Find the domain of the function. f(x) = 1 x (, 4) ( 4, ) (, 1) ( 1, ) (, 4] (, 1] ID:.6-5

11 11 of 39 1/18/017 10:43 AM 31. Given functions f and g, find f g. f(x) =9x 7, g(x) =4x 9 5 x + 13x 16 5x 16 5x ID: f Given functions f and g, find. g f(x) =5x 8 x, g(x) =x 4x 3 5x x+1 5 x 3 5x 8 4 5x 8x x 4x 3 ID: Given functions f and g, find f + g. f(x) =7 5 x, g(x) = x +5 x +7 3 x +1 7 x +1 5x ID: Given functions f and g, find fg. f(x) =5x 6, g(x) =8 x +9 13x 3 x +3 40x 39x 54 40x 3x 54 40x 54 ID:.6-1

12 1 of 39 1/18/017 10:43 AM 35. For the given functions f and g, find the indicated composition. f(x) = 4 x +5, g(x) =5 x +4; (g f)(x) 0 x +1 0 x + 9 0x 1 0 x +9 ID: For the given functions f and g, find the indicated composition. f(x) = 5, g(x) = ; (f g)(x) x 4 7x x 8 35x 5x 8x 35x 8x 35x + 8x ID: For the given functions f and g, find the indicated composition. f(x) = x 10, g(x) =8 x +10; (g f)(x) 8 x 5 4 x 8 x +70 x +0 ID:.6-5

13 13 of 39 1/18/017 10:43 AM 38. Find the distance between the pair of points. (, ) and ( 147, ) ID: Find the midpoint of the line segment whose end points are given. ( 4, 8) and ( 93, ) 5, 11 ( 13, 5) 13 5, (5, 11) ID: Graph the equation, and find the domain and range. (x 4) +(y 5) =4 Domain: [ 6, ], Range: [ 7, 3] Domain: [ 6, ], Range: [ 37, ] ID:.8-14

14 14 of 39 1/18/017 10:43 AM 41. Complete the square and write the equation in standard form. Then give the center and radius of the circle. x +14 x+49+y 8 y+16=16 (x 4) +(y+7) =16 Center: ( 47, ), radius: 16 (x + 7) +(y 4) =16 Center: ( 74, ), radius: 4 (x + 7) +(y 4) =16 Center: ( 7 4, ), radius: 16 (x 4) +(y+7) =16 Center: ( 4 7, ), radius: 4 ID: Use the vertex and intercepts to sketch the graph of the quadratic function. f(x) = x 4 x +5 ID: Use the vertex and intercepts to sketch the graph of the quadratic function. f(x) =x x 8 ID: 3.1-5

15 15 of 39 1/18/017 10:43 AM 44. The profit that the vendor makes per day by selling x pretzels is given by the function number of pretzels that must be sold to maximize profit. P(x) = 4x +,400x 350. Find the 600 pretzels 300 pretzels 1,00 pretzels 359,650 pretzels ID: An arrow is fired into the air with an initial velocity of 18 feet per second. The height in feet of the arrow t seconds after it was shot into the air is given by the function h(x) = 16t + 18t. Find the maximum height of the arrow. 64 ft 448 ft 56 ft 768 ft ID: April shoots an arrow upward into the air at a speed of 3 feet per second from a platform that is 34 feet high. The height of the arrow is given by the function h(t) = 16t +3 t +34, where t is the time is seconds. What is the maximum height of the arrow? 50 ft 34 ft 33 ft 16 ft ID: Graph the polynomial function. f(x) =x 3 +9x x 9 ID: 3.-46

16 16 of 39 1/18/017 10:43 AM 48. Find the zeros of the polynomial function. f(x) =x 3 +x 6x x= 0, x =1, x= x = 3, x= x =1, x= x= 0, x = 3, x= ID: Find the zeros of the polynomial function. f(x) =x 3 +4x x 4 x= 1, x = 4, x=4 x=16 x = 1, x = 1, x = 4 x = 4, x=4 ID: Use synthetic division to show that the number given to the right of the equation is a solution of the equation, then solve the polynomial equation. x 3 5x x+4= 0; 4 { 34,, } { 3 4,, } { 34,, } { 3, 4, } ID: 3.3-4

17 17 of 39 1/18/017 10:43 AM 51. Use the graph or a table to determine a solution of the equation. Use synthetic division to verify that this number is a solution of the equation. Then solve the polynomial equation. x 3 + 6x + 11x+ 6= 0 1; The remainder is zero; 1,, and 3, or { 3, 1,} 1; The remainder is zero; 1,, and 3, or { 3,, 1} 1; The remainder is zero; 1,, and 3, or {, 1,3} 1; The remainder is zero; 1,, and 3, or { 3,,1} ID: Find a rational zero of the polynomial function and use it to find all the zeros of the function. f(x) =x 3 +x 5x 6 { 1} { 3, 1, } { 3} {, 1, 3} ID: Find a rational zero of the polynomial function and use it to find all the zeros of the function. f(x) =x 3 +6x +5x 6 {1, 1, 6} {, + 7, 7 } {, 4+ 7, 4 7 } {, 4+ 6, 4 6 } ID:

18 18 of 39 1/18/017 10:43 AM 54. Find a rational zero of the polynomial function and use it to find all the zeros of the function. f(x) =x 3 x +5 x +6 {, +3i, 3i} {, 3+i, 3 i} {, + 5, 4 5 } {, 3+ 5, 3 5 } ID: Solve the polynomial equation. In order to obtain the first root, use synthetic division to test the possible rational roots. x 3 +3x 4x 1= 0 { } { 3} {,, 3} { 3,, } ID: Find the vertical asymptotes, if any, of the graph of the rational function. x g(x) = x 9 x =3, x = 3, x= 0 x =3, x= 3 x=3 no vertical asymptote ID: Find the horizontal asymptote, if any, of the graph of the rational function. g(x) = 8x 3x 5 3x 6x+9 y= 0 y = 8 3 y = 1 no horizontal asymptote ID:

19 19 of 39 1/18/017 10:43 AM 58. Find the slant asymptote, if any, of the graph of the rational function. f(x) = x 7x+5 x+6 x= y+7 y= x+1 y= x 13 no slant asymptote ID: A city is growing at the rate of 0.7% annually. If there were 3,87,000 residents in the city in 199, find how many (to the nearest ten-thousand) are living in that city in 000. Use y = 3,87,000(.7) 0.007t. 3,510, ,000 8,870,000 3,480,000 ID: The size of the coyote population at a national park increases at the rate of 5% per year. If the size of the current population is 185, find how many coyotes there should be in 5 years. Use the function f(x) = t and round to the nearest whole number ID: Find the domain of the logarithmic function. f(x) = log (x + 1) 3 ( 1, ) (,0) or (0, ) ( 1, ) ( 3, ) ID: 4.-31

20 0 of 39 1/18/017 10:43 AM 6. Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. log b xy z 3 3 log bx+ log b y log bz log x+log y+3log z b b b 3 log bx+ log b y + log bz log x+log y 3log z b b b ID: Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. 5 m 4 n log 9 k 5 log m+4log n log k log m log n log k log m+ log n log k log m+ log n log k ID: Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. log a x 4 3 x+5 (x ) 4 log x 3log (x + 5) log ( x ) a a a 1 4 log ax+ log (x + 5) log (x ) 3 a a log ax + log a(x + 5) log a(x ) 4 3 log ax + log a(x + 5) log a(x ) ID: 4.3-

21 1 of 39 1/18/017 10:43 AM 65. Solve the equation by expressing each side as a power of the same base and then equating exponents. 3 (1 + x) =43 { 6} { } { 81} { } ID: Solve the equation by expressing each side as a power of the same base and then equating exponents. 4 (5 3x) = 1 56 { 18} 1 64 { 3} { 3} ID: Solve the equation by expressing each side as a power of the same base and then equating exponents. 4 (3x + 7) = 1 16 { 3} { 3} { 4} 1 4 ID: 4.4-3

22 of 39 1/18/017 10:43 AM 68. Solve the exponential equation. Express the solution set in terms of natural logarithms. 7 9x = ln 9 ln 7 ln ln 9 ln ln 7 9 ln 4.5 ln 7 ID: Solve the exponential equation. Express the solution set in terms of natural logarithms. x+7 =3 ln 3 ln ln 7 ln 3 ln 7 ln ln 3 +7 ln ln 3 + ln 7 ID: Solve the exponential equation. Express the solution set in terms of natural logarithms. x+7 =5 5 { +7 } ln 1 35 { } ln 5 7 ID:

23 3 of 39 1/18/017 10:43 AM 71. Solve the exponential equation. Use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. 10 x = ID: Solve the exponential equation. Use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. 5 x = ID: Solve the exponential equation. Use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. 6 4x = ID: Solve the exponential equation. Use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. 3x = ID:

24 4 of 39 1/18/017 10:43 AM 75. Solve the logarithmic equation. Be sure to reject any value that is not in the domain of the original logarithmic expressions. Give the exact answer. log (x 5) + log (x 11)= 4 4 { 13, 3} { 14} { 13} { 3} ID: Solve the logarithmic equation. Be sure to reject any value that is not in the domain of the original logarithmic expressions. Give the exact answer. log 5(x + ) log 5 x = { 5} 1 1 { 1} 5 ID: Solve the logarithmic equation. Be sure to reject any value that is not in the domain of the original logarithmic expressions. Give the exact answer. ln 6+ ln (x 1) = { 1} 7 6 ID: 4.4-9

25 5 of 39 1/18/017 10:43 AM 78. Solve the logarithmic equation. Be sure to reject any value that is not in the domain of the original logarithmic expressions. Give the exact answer. log (x + ) 5 log (x 3) 5 = ID: Solve the logarithmic equation. Be sure to reject any value that is not in the domain of the original logarithmic expressions. Give the exact answer. log ( + x) log (x 3) = log { 8} { 8} 3 ID: Solve the logarithmic equation. Be sure to reject any value that is not in the domain of the original logarithmic expressions. Give the exact answer. log ( + x) log (x 3) = log { 8} 3 { 8} ID:

26 6 of 39 1/18/017 10:43 AM 81. Solve the logarithmic equation. Be sure to reject any value that is not in the domain of the original logarithmic expressions. Give the exact answer. ln x+ ln (x 1) = ln { 7} { 8} { 8, 7} ID: Solve the logarithmic equation. Be sure to reject any value that is not in the domain of the original logarithmic expressions. Give the exact answer. ln x+ ln (x 1) = ln { 5} { 6, 5} { 6} ID: Find out how long it takes a $ 3,500 investment to double if it is invested at 9% compounded quarterly. Round to the nearest tenth of a year. Use the formula A=P 1+ r nt. n 8.0 years 7.8 years 8. years 7.6 years ID: The size of the coyote population at a national park increases at the rate of 5% per year. If the size of the current 0.05t population is 159, find how many coyotes there should be in 7 years. Use y = y o and round to the nearest whole number ID:

27 7 of 39 1/18/017 10:43 AM x The function A =A 0 models the amount in pounds of a particular radioactive material stored in a concrete vault, where x is the number of years since the material was put into the vault. If 00 pounds of the material are initially put into the vault, how many pounds will be left after 30 years? Round to nearest whole number. 67 pounds 38 pounds 154 pounds 31 pounds ID: x The function A =A 0 models the amount in pounds of a particular radioactive material stored in a concrete vault, where x is the number of years since the material was put into the vault. If 00 pounds of the material are placed in the vault, how much time will need to pass for only 11 pounds to remain? Round to nearest whole number. 55 years 50 years 100 years 60 years ID: The half-life of silicon-3 is 710 years. If 90 grams is present now, how much will be present in 800 years? (Round your answer to three decimal places.) ID: The population of a certain country is growing at a rate of 1.9% per year. How long will it take for this country's population ln to double? Use the formula t= k, which gives the time, t, for a population with growth rate k, to double. (Round to the nearest whole year.) 38 years 36 years 37 years 35 years ID: 4.5-8

28 89. Solve the system of equations. 4x + 4y + z = 11 4x 3y z = 30 4x+y+3z = {(3, 3, 5) } {(3, 5, 3) } {( 5, 3, 3) } {( 3, 5, 3) } ID: Solve the system by the substitution method. x y = 3 x = y +39 {(8, 5)} {(8, 5)} {( 8, 5)} {( 8, 5)} ID: Solve the system of equations using matrices. Use Gaussian elimination with back-substitution. x+ y+ z = 5 x y+ z = 6 3x + y + z = 1 {( 5,, )} {( 5,, )} {(,, 5)} {(, 5, )} ID: of 39 1/18/017 10:43 AM

29 9 of 39 1/18/017 10:43 AM 9. Find the product AB, if possible. A = , B = AB is not defined ID: Evaluate the determinant ID: Use Cramer's rule to solve the system. x + 5y z = 48 x 5y+4z = 1 5 x+ y+ z = 34 {( 495,, )} {( 959,, )} {( 4 9 5,, )} {( 575,, )} ID: 6.5-1

30 30 of 39 1/18/017 10:43 AM 95. Find the indicated sum. 6 i=3 6i ID: Find the indicated sum. 6 i=3 (3i 4) ID: Find the indicated sum. 4 i i= ID: Use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum. 47 i=1 (4i 5) 4,77 4,183 4, ,606 ID: 8.-8

31 31 of 39 1/18/017 10:43 AM 99. Find the indicated sum. Use the formula for the sum of the first n terms of a geometric sequence. 5 i 4 4 i=1 1,360 5, ,80 ID: Use the Binomial Theorem to expand the binomial and express the result in simplified form. (3x + ) 3 3 7x + 54x + 54x x + 54x + 36x + 8 9x + 1x x + 6x + 64 ID: Use the Binomial Theorem to expand the binomial and express the result in simplified form. (x + 3) x + 88x + 16x + 648x x + 81x 3 16x + 96x + 16x x + 96x + 16x + 16x + 81 ID: Write the first three terms in the binomial expansion, expressing the result in simplified form. (x + ) x + 3x + 1,088x x + 34x + 1,088x x +34x +544x x +3x +544x ID: 8.5-1

32 3 of 39 1/18/017 10:43 AM i i { 15, } , {,1} 7. { 6±6i} 8. { 18, } , { 6 4i, 6+4i} , , { 7 11, } 14. { 1,1, 4}

33 33 of 39 1/18/017 10:43 AM 15. { 3} 16. { 8, 5} 17. {9} , ( 1, ) 0. (, ] [ 6, ) 1. Maximum: (0,1); minimum: (, 3). Minimum: (, 14) Maximum: (,18) x + h + 6.

34 34 of 39 1/18/017 10:43 AM (, 1] x x 8x x 4x x x 3x x x 8x 37. x

35 35 of 39 1/18/017 10:43 AM , Domain: [, 6], Range: [ 3, 7] 41. (x + 7) +(y 4) = 16Center: ( 74, ), radius: pretzels ft ft

36 36 of 39 1/18/017 10:43 AM x = 0, x = 3, x = 49. x = 1, x = 1, x = { 3 4,, } 51. 1; The remainder is zero; 1,, and 3, or { 3,, 1} 5. { 3, 1, } 53. {, + 7, 7 } 54. {, +3i, 3i} 55. { 3,, } 56. x =3, x = y = y = x ,480, ( 1, ) 6. log x+log y 3log z b b b

37 log m+ log n log k log a x+ log (x + 5) log (x ) 3 a a 65. { } 66. { 3} 67. { 3} 68. ln ln ln 3 ln ln { 13} of 39 1/18/017 10:43 AM

38 38 of 39 1/18/017 10:43 AM 79. { 8} 80. { 8} 81. { 8} 8. { 6} years pounds years years 89. {(3, 5, 3) } 90. {(8, 5)} 91. {(,, 5)} {( 495,, )}

39 39 of 39 1/18/017 10:43 AM , , x + 54x + 36x x + 96x + 16x + 16x x + 34x + 544x

Mock Final Exam Name. Solve and check the linear equation. 1) (-8x + 8) + 1 = -7(x + 3) A) {- 30} B) {- 6} C) {30} D) {- 28}

Mock Final Exam Name. Solve and check the linear equation. 1) (-8x + 8) + 1 = -7(x + 3) A) {- 30} B) {- 6} C) {30} D) {- 28} Mock Final Exam Name Solve and check the linear equation. 1) (-8x + 8) + 1 = -7(x + 3) 1) A) {- 30} B) {- 6} C) {30} D) {- 28} First, write the value(s) that make the denominator(s) zero. Then solve the