[PDF] Skills Practice Skills Practice. Multiplying and Dividing

View - Download Skills Practice

Previous PDF

Next PDF

Skills Practice

Multiplying and Dividing Rational Expressions

NAME ______________________________________________ DATE ____________ PERIOD _____

9-19-1

Glencoe/McGraw-Hill519Glencoe Algebra 2

Lesson 9-1

Simplify each expression.

1.2. 3. x64. 5.6. 7.8.? 9.?

6e10.?

11.

4?1g312.4

13.4 x(x22)14.4

15.?16.?

(w28)(w27)

17.4(3x??3x)18.4

19.

220.a2b}

?a? 4? ab ?a ab?5} ??c d ??5c d 6?

1}x??5x?4???x?8

t112}?t????t??9t?14t ??19t?84??4t?4w ??6w?7??w?3w ??5w??4??w?1 q2 }q??4?3q?q? ??q?6q3x?x??43x??x??

32z7}?5y5?14z1?v580y4?49z5v7

1}7g?y?

1}}s???10s55s??

s??410(ef)3?8e5f?4e3?5f? mn2}n3?63m??n a28}3a???4a??3a??1?a x12}x??4??(x??)(x ?1)9}18??x?6

2}8y?(y6)3?4y?4(x6)3?(x3)4

b}5ab3??5a?b?

3x}?1x3y?14x?y?

Skills Practice

Adding and Subtracting Rational Expressions

NAME ______________________________________________ DATE ____________ PERIOD _____

9-29-2

Glencoe/McGraw-Hill525Glencoe Algebra 2

Lesson 9-2

Find the LCM of each set of polynomials.

1.??c? 6c

?d12c2d2.?8a3bc?? ?4b?c?72a3b2c2

3.?x26?x232(x23)4.?a?a2?5a(a21)

Simplify each expression.

7.18.1

9.1410.1

11.212.1

13.214.2

15.216.1

17.218.1

19.120.2

21.122.2

y112}}}n12} ?}}y?16y183}}y?1y2???n1?}}n?2?n23n}n23

2x215x22}}4}}x?23x2?0?x1?}x2?

x21x11}}x}x1??}}x?1?x1?

5z214z216}}z14}z1?4z}z24

2m}m}n2mm}m2n

523t}?}x2?3t}? 2x

3w17}}?}w?293}w23

15bd26b22d}}?}3bd?}3b1d

a26}}3}?a?}a1?

7h13g}}3}4h?7}4gh

12z22y}}?}?yz??}?y?

215m2}}?}n?}m?n

2c15}?c27}3

13}?}4p?q3}8p?q

5x13y}?}y3}x

Study Guide and Intervention

Graphing Rational Functions

NAME ______________________________________________ DATE ____________ PERIOD _____

9-39-3

Glencoe/McGraw-Hill529Glencoe Algebra 2

Lesson 9-3

Vertical Asymptotes and Point Discontinuity

Rational Functionan!equation!of!the!form!f(x)!5,!where!p(x)!and!q(x)!are!polynomial!expressions!and! q(x)!Þ0

Vertical Asymptote An!asymptote!is!a!line!that!the!graph!of!a!function!approaches,!but!never!crosses.!

of the Graph of a If!the!simplified!form!of!the!related!rational!expression!is!undefined!for! x5a,!

Rational Functionthen!x5ais!a!vertical!asymptote.

Point Discontinuity Point!discontinuity!is!like!a!hole!in!a!graph.!If!the!original!related!expression!is!undefined!!

of the Graph of a for!

Rational Functiongraph!at!

x5a. Determine the equations of any vertical asymptotes and the values of xfor any holes in the graph of f(x) 5? First factor the numerator and the denominator of the rational expression. f(x) 5 5

The function is undefined for x51 and x5 21.

Since 5,x51 is a vertical asymptote. The simplified expression is defined for x5 21, so this value represents a hole in the graph. Determine the equations of any vertical asymptotes and the values of xfor any holes in the graph of each rational function? ??f(x) 5??f(x) 53?f(x) 5 asymptotes:x52, hole: x5asymptote:x50; x5 25holex54

4?f(x) 5??f(x) 56?f(x) 5

asymptote:x5 22; asymptotes: x51, asymptote: x5 23 hole: x5x5 27

7?f(x) 58?f(x) 59?f(x) 5

asymptotes:x51, asymptote: x5 23; holes: x51,x53 x55hole:x53} 1}

3x225x22}}x13x

226x27}}x216x273x21}}3x215x22

5} }x21(4x23)(x11)}}(x11)(x21)(4x23)(x11) }}(x11)(x21)4x21x23}}x2214x?1x23 }}x?2? p(x)}q(x)

ExampleExample

ExercisesExercises

Assignment ___________________________

Skills Practice

Graphing Rational Functions

NAME ______________________________________________ DATE ____________ PERIOD _____

9-39-3

Glencoe/McGraw-Hill531Glencoe Algebra 2

Lesson 9-3

Determine the equations of any vertical asymptotes and the values of xfor any holes in the graph of each rational function.

1.f(x) 52.f(x) 5

asymptotes:x54,x5 22 asymptotes:x54,x59

3.f(x) 54.f(x) 5

asymptote:x52; hole: x5 212 asymptote: x53; hole: x51

5.f(x) 56.f(x) 5

hole:x5 22 hole:x53

Graph each rational function.

7.f(x) 58.f(x) 59.f(x) 5

10.f(x) 511.f(x) 512.f(x) 5

xO f(x) xO f(x) xO f(x) x224}x22x}x122}x21 xO f(x) xO f(x) 2 2 xO f(x)

24}x10}x23}xx

21x212

}}x23x

218x112}}x12x21

}}x224x13x112}}x2110x22410 }}x2213x1363}}x222x28

©Glencoe/McGraw-Hill538Glencoe Algebra 2

State whether each equation represents a direct,joint, or inversevariation. Then name the constant of variation.

1.u58wz

joint; 82.p54sdirect; 43.L5 inverse; 54.xy54.5 inverse; 4.5

5.5 p6.2d5mn7.5h8.y5

direct;pjoint; inverse; 1.25 inverse;

Find each value.

9.If yvaries directly as xand y58 when x52, find ywhen x56.

24

10.If yvaries directly as xand y5 216 when x56, find xwhen y5 24.1.5

11.If yvaries directly as xand y5132 when x511, find ywhen x533.396

12.If yvaries directly as xand y57 when x51.5, find ywhen x54.

13.If yvaries jointly as xand zand y524 when x52 and z51, find ywhen x512

and z52. 288

14.If yvaries jointly as xand zand y560 when x53 and z54, find ywhen x56

and z58. 240

15.If yvaries jointly as xand zand y512 when x5 22 and z53, find ywhen x54

and z5 21. 8

16.If yvaries inversely as xand y516 when x54, find ywhen x53.

17.If yvaries inversely as xand y53 when x55, find xwhen y52.5.

6

18.If yvaries inversely as xand y5 218 when x56, find ywhen x55.?21.6

19.If yvaries directly as xand y55 when x50.4, find xwhen y537.5.3

20.GASESThe volume Vof a gas varies inversely as its pressure P. If V580 cubic

centimeters when P52000 millimeters of mercury, find Vwhen P5320 millimeters of mercury.

500 cm3

21.SPRINGSThe length Sthat a spring will stretch varies directly with the weight Fthat

is attached to the spring. If a spring stretches 20 inches with 25 pounds attached, how far will it stretch with 15 pounds attached?

12 in.

22.GEOMETRYThe area Aof a trapezoid varies jointly as its height and the sum of its

bases. If the area is 480 square meters when the height is 20 meters and the bases are

28 meters and 20 meters, what is the area of a trapezoid when its height is 8 meters and

its bases are 10 meters and 15 meters?

100 m264

56?
3?1?

3}4x1.25}gC}d5

}kPractice (Average)

Direct, Joint, and Inverse Variation

NAME ______________________________________________ DATE ____________ PERIOD _____

9-?9-?

Study Guide and Intervention

Classes of Functions

NAME ______________________________________________ DATE ____________ PERIOD _____

9-59-5

Glencoe/McGraw-Hill541Glencoe Algebra 2

Lesson 9-5

Identify GraphsYou should be familiar with the graphs of the following functions.

Function Description of Graph

Direct Variationa!line!that!passes!through!the!origin!and!is!neither!horizontal!nor!vertical

Greatest Integera!step!function

Absolute ValueV-shaped!graph

Quadratica!parabola

Square Roota!curve!that!starts!at!a!point!and!curves!in!only!one!direction

Inverse Variation

Identify the function represented by each graph?

1? ?? 3?

quadratic rational direct variation

4? 5? 6?

constant absolute value greatest integer

7? 8? 9?

identity square root inverse variation xyO xyO xyO xyOxyO xyO xyOxyO xyO

ExercisesExercises

©Glencoe/McGraw-Hill542Glencoe Algebra 2

Identify EquationsYou should be able to graph the equations of the following functions.

Function General Equation

Constanty5a

Direct Variationy5ax

Identityy5x

Greatest Integerequation includes a variable within the greatest integer symbol, vb Absolute Valueequation includes a variable within the absolute value symbol, ||

Quadraticy5ax21bx1c, where aÞ0

Rationaly5

Inverse Variation

y5 Identify the function represented by each equation.Then graph the equation. ?.y5 inverse variation?.y5xdirect variation3.y5 2quadratic

4.y5|3x|21absolutevalue?.y5 2inverse variation6.y59 0greatestinteger

xyOxyOxyO x215x16}}x12 xyOxyOxyO x}22}x xyOxyO xyO x2}24}36}x a}xp (x)}q(x)Study Guide and Intervention (continued)

Classes of Functions

NAME ______________________________________________ DATE ____________ PERIOD _____

9-59-5

ExercisesExercises

Skills Practice

Solving Rational Equations and Inequalities

NAME ______________________________________________ DATE ____________ PERIOD _____

9-69-6

Glencoe/McGraw-Hill549Glencoe Algebra 2

Lesson 9-6

Solve each equation or inequality. Check your solutions. 1.? ?12.2 ? ? 3.? ?14.3 ?z?1, 2

5.?56.??5, 8

7.??38.? ?y?73, 4

9.?810.? ?0k?0

11.2 ? ?0?v?412.n? ?n? ?3 or 0 ?n?3

13.? ? ?0?m?114.? ?10?x?

15.? ?9316.?4 ?4

17.2 ? ??518.8 ? ?

19.? ?

?420.? ??

21.? ??22.? ?2

23.? ??624.? ?52?t?34?t?38?t2?92?e?21?e?22e?e2?45

?w2?41?w?21?w?22?n?35?n2?91?n?3

2?8z?8?z?24?z2q?q?15?2qb?2

?b?13b?2?b?19x?7?x?215?x

3?2?x1?2x5?23?m1?2m12

?n3?n5?v3?v4 ?3k3?kx?1?x?10x?2?x?412 ?y3?22x?3?x?18 ?ss?3?51?d?22?d? 12 ?z?6?29?3x

12?1?34?n1?2x?x?1

© Glencoe/McGraw-Hill372Glencoe Algebra 2

Chapter 6 Cumulative Review

(Chapters 1-6)

1.Find the value of 12136442(527)2.(Lesson 1-1)1.

2.Find the slope of the line that is parallel to the line with 2.equation 3x14y510.(Lesson 2-3)

3.Describe the system 2x23y521 and y255

}2

3}xas 3.

consistent and independent,consistentand dependent, or inconsistent.(Lesson 3-1)

4.Find the coordinates of the vertices of the figure formed 4.

by the system of inequalities.(Lesson 3-3) x$ 22x1y#6 y$ 22x1y$ 22

5. Find the value of ) ).(Lesson 4-5)5.

6.Solve ? ??? ?5? ?by using inverse matrices.6.

(Lesson 4-8)

7.Use synthetic division to find 7.

(2x

415x32x2110x14)4(x13).(Lesson 5-3)

wto three 8.decimal places.(Lesson 5-5) w1158.(Lesson 5-8)9. 10.

PHYSICSAn object is thrown straight up from the top of 10.a 100-foot platform at a velocity of 48 feet per second. The

height h(t) of the object tseconds after being thrown is given by h(t)5 216t

2148t1100. Find the maximum

height reached by the object and the time it takes to achieve this height.(Lesson 6-1)

11.Solve x

252x13 by graphing.(Lesson 6-2)11.

12.Solve 4x

224x524 by factoring.(Lesson 6-3)12.

13.Find the value of the discriminant for 7x

215x1150.13.

Then describe the number and type of roots for the equation.(Lesson 6-5)

14.Write y5x

227x15 in vertex form.(Lesson 6-6)14.

y x O 11 213a
b21 34
22
12 45
26

NAME DATE PERIOD

66

© Glencoe/McGraw-Hill570Glencoe Algebra 2

Chapter 9 Cumulative Review

(Chapters 1-9)

1.Determine whether C?? ?and D?? ?are 1.

inverses.(Lesson 4-7)

2.Simplify the expression ?w

?1 3?? ?2 5? .(Lesson 5-7)2.

3.Solve x

2?2x?2?0 by completing the square.(Lesson 6-4)3.

4. Graph y?x

2?4x.(Lesson 6-7)4.

5.Use synthetic substitution to find f(3) for 5.

f(x)?3x

3?7x2?5x?10.(Lesson 7-4)

6.List all of the possible rational zeros of 6.

2x

4?5x3?3x2?12x?6.(Lesson 7-6)

7.Write an equation for a circle with center at (0,?3) that 7.

passes through (5, 7).(Lessons 8-1 and 8-3)

8.Write an equation for the ellipse whose major axis is 8.

10 units long and parallel to the x-axis, whose minor axis is

6 units long, and whose center is at (1,?2).(Lesson 8-4)

9.State whether the graph of 5x

2?5y2?10x?15y?10 is an 9.

ellipse,circle,parabola, or hyperbola.(Lesson 8-6)

10.Simplify .(Lesson 9-1)10.

11.Suppose yvaries jointly as xand z. Find ywhen x?16 and 11.

z?5, if y?9 when x?3 and z?12.(Lesson 9-4)

12.Evita adds a 75% acid solution to 8 milliliters of solution 12.

that is 15% acid. The function that represents the percent of acid in the resulting solution is f(x)? ?8(0.15 8)? ?x x(0.75) where xis the amount of 75% acid solution added. How much 75% acid solution should be added to create a solution that is 50% acid?(Lesson 9-6) ?59 yy22?? 13 06 y? ?106 yy2? ?1 22
0y? y x O ?11 6? ??15 6? 1 5 ?3 1

NAME DATE PERIOD

99
quotesdbs_dbs9.pdfusesText_15

[PDF] 8 6 skills practice solving rational equations and inequalities answers with work

[PDF] 8 6 skills practice the law of cosines

[PDF] 8 6 skills practice the law of cosines answers

[PDF] 8 6 skills practice the law of sines

[PDF] 8 6 skills practice the law of sines answer key

[PDF] 8 6 skills practice the law of sines answers

[PDF] 8 6 skills practice using the distributive property

[PDF] 8 6 study guide and intervention

[PDF] 8 6 study guide and intervention factoring quadratic trinomials

[PDF] 8 6 study guide and intervention factoring quadratic trinomials answers

[PDF] 8 6 study guide and intervention rational equations

[PDF] 8 6 study guide and intervention the law of sines and law of cosines

[PDF] 8 6 study guide and intervention the law of sines and the law of cosines answer key

[PDF] 8 6 study guide and intervention the law of sines answers

[PDF] 8 6 study guide and intervention trapezoids answer key