Infinite Algebra 2 - Chapter 6 Test Review

Algebra 2/Trig

Name___________________________________ ID: 1

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Chapter 6 Test Review

Date________________ Period____

Simplify. Your answer should contain only positive exponents with no fractional exponents in the denominator. -

1) ( y ) × ( x y ) -

2 2

-2

4 3

3)

2y × y 4xy × 4x

3 2

2 3

2) yx

y

4)

3 2

×x

2

1 2

2

( ) -

2

5 3

-2

x

1 3

x y

5 3

Solve each equation. Remember to check for extraneous solutions. 5)

x + 9 + 8 = 10

7)

2v - 1 = 1 +

6) 1 =

3v - 3

8)

6x - 2 - x

1 - 6a =

3a + 10

Find the inverse of each function. 9) f ( x) =

5

x+1-2

1 5 10) f ( x) = x + 2 2

3

11) f ( x) = ( x + 1) + 3

12) f ( x) =

3

x+1 2

Worksheet by Kuta Software LLC

-1-

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State if the given functions are inverses. 13) g( x) = x - 2 12 - x f ( x) = 3

3 x-2 3 f ( x) = + 2 x

14) g( x) =

Perform the indicated operation. 15) g( x) = x 2 - 4 h( x ) = x + 3 Find ( g h)( x)

16) h( x) = 3x 3 + x g( x) = -2x - 3 Find (4h + 4g)( x)

Identify the domain and range of each. Then sketch the graph. 17) y =

x-4+1

18) y =

x+4

y

-8

-6

19) y =

-4

y

8

8

6

6

4

4

2

2

-2

2

4

6

8 x

-8

-6

-4

-2

-2

-2

-4

-4

-6

-6

-8

-8

x-3+3

20) y =

-6

-4

6

8 x

2

4

6

8 x

y

8

8

6

6

4

4

2

2

-2

4

x+6

y

-8

2

2

4

6

8 x

-8

-6

-4

-2

-2

-2

-4

-4

-6

-6

-8

-8

Worksheet by Kuta Software LLC

-2-

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Algebra 2/Trig

Name___________________________________ ID: 1

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Chapter 6 Test Review

Date________________ Period____

Simplify. Your answer should contain only positive exponents with no fractional exponents in the denominator. -

1) ( y ) × ( x y ) -

2 2

-2

3 2

2 3

2) yx

-2

×x

2

1 2

2

y

4 5 3

y x

4 3

3)

2y × y 4xy × 4x 2 3

x y 8

5 3

( ) -

2

y

4)

3 2

x

1 3

x y

5 6

5 3

1 3

2 3

x y x2y4 Solve each equation. Remember to check for extraneous solutions. 5)

x + 9 + 8 = 10

{-5}

7)

6x - 2 - x

6) 1 =

{3, 1}

2v - 1 = 1 +

3v - 3

8)

{1 }

1 - 6a =

3a + 10

{-1}

Find the inverse of each function. 9) f ( x) = f

5

x+1-2

-1

( x) = ( x + 2) 5 - 1

1 5 10) f ( x) = x + 2 2 f

-1

( x) = 2x - 5

3

11) f ( x) = ( x + 1) + 3 f

-1

( x) =

3

12) f ( x) =

x-3-1 f

-1

3

x+1 2

( x) = 2x 3 - 1

Worksheet by Kuta Software LLC

-1-

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State if the given functions are inverses. 13) g( x) = x - 2 12 - x f ( x) = 3

3 x-2 3 f ( x) = + 2 x

14) g( x) =

No

Yes

Perform the indicated operation. 15) g( x) = x 2 - 4 h( x ) = x + 3 Find ( g h)( x)

16) h( x) = 3x 3 + x g( x) = -2x - 3 Find (4h + 4g)( x)

x 2 + 6x + 5

12x 3 - 4x - 12

Identify the domain and range of each. Then sketch the graph. 17) y =

x-4+1

18) y =

y

-6

19) y =

-4

6

4

4

2

2

-2

2

4

6

-4

-8

-6

-4

-2

2 -2

-4

-4

-6

-6

-8

-8

20) y =

y

-6

8 x

-2

x-3+3

4

4

2

2 6

8 x

-8

-6

8 x

Domain: x ³ -6 Range: y ³ 0

8 6

4

6

y

Domain: x ³ 3 Range: y ³ 3

2

4

x+6

6

-2

Domain: x ³ -4 Range: y ³ 0

8

6

8

-8

y

Domain: x ³ 4 Range: y ³ 1

8

-8

x+4

-4

-2

2

-2

-2

-4

-4

-6

-6

-8

-8

4

6

8 x

Worksheet by Kuta Software LLC

-2-

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