Algebra 2 Name ALT 2: Functions

ALT 2 Review Tell whether the relation is a function, then give the domain and range. 1. 2. 3. Domain: Domain: Domain: Range: Range: Range: Identify the domain and range of each relation. Then represent the relation using a mapping diagram. Finally, tell whether the relation is a function. 4. 5. Domain: Domain: Range: Range Function: Yes No Function: Yes No Use the vertical line test to tell whether the relation is a function. 6. 7. Function: Yes No Function: Yes No

Algebra 2 Name:

2.1 and 2.2 Worksheet

Functions and Lines

The following exercises are based on the lessons 2.1 and 2.2 in your textbook. Please refer to your class notes and pages

72-76 and 82-85 in your textbook if you have any difficulty.

For exercises 1-4, identify the domain and range of the relation below. Then represent the relation using a mapping diagram.

Finally, decide whether or not the relation is a function.

1. (�2, 3), (1, 2), (3,�1), (�4,�3) 2. (5,�2), (�3,�2), (3, 3), (�1,�1)

3. (4,�2), (4, 2), (16,�4), (16, 4) 4. (5, 20), (10, 20), (10, 30), (20, 30)

For exercises 5-7, use the vertical line test to decide whether the graph is the graph of a function.

5. 6. 7.

x

y

-5 5

-4

4

x

y

x

y

For exercises 8-13, evaluate the function at the given value.

8. Let f(x) = x+ 15. Evaluate f(8). 9. Let f(x) = x

2 + 1. Evaluate f(�3).

10. Let f(x) = |x|+ 10. Evaluate f when x = �4. 11. Let f(x) = 6. Evaluate f when x = 2.

12. Let g(x) = x

3 � 2x2 + 5x� 8. Evaluate g(�5). 13. Let h(x) = 7� 2

3x. Evaluate h(15).

1 of 2

Algebra 2 Name:

2.1 and 2.2 Worksheet

Functions and Lines

The following exercises are based on the lessons 2.1 and 2.2 in your textbook. Please refer to your class notes and pages

72-76 and 82-85 in your textbook if you have any difficulty.

For exercises 1-4, identify the domain and range of the relation below. Then represent the relation using a mapping diagram.

Finally, decide whether or not the relation is a function.

1. (�2, 3), (1, 2), (3,�1), (�4,�3) 2. (5,�2), (�3,�2), (3, 3), (�1,�1)

3. (4,�2), (4, 2), (16,�4), (16, 4) 4. (5, 20), (10, 20), (10, 30), (20, 30)

For exercises 5-7, use the vertical line test to decide whether the graph is the graph of a function.

5. 6. 7.

x

y

-5 5

-4

4

x

y

x

y

For exercises 8-13, evaluate the function at the given value.

8. Let f(x) = x+ 15. Evaluate f(8). 9. Let f(x) = x

2 + 1. Evaluate f(�3).

10. Let f(x) = |x|+ 10. Evaluate f when x = �4. 11. Let f(x) = 6. Evaluate f when x = 2.

12. Let g(x) = x

3 � 2x2 + 5x� 8. Evaluate g(�5). 13. Let h(x) = 7� 2

3x. Evaluate h(15).

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Determine the domain and range of each relation. 8. 9. Domain: Domain: Range: Range: 10. 11. Domain: Domain: Range: Range: 12. 13. Domain: Domain: Range: Range:

Directions: For each absolute value function give the coordinates of the vertex, whether it opens up or down, and if it is narrower, wider, or the same width as y = x . Then graph each function.

14. y = x − 4 +1 15. y = − 23x − 2

vertex: vertex: opens: up down opens: up down narrower wider same width narrower wider same width

16. 𝒇 𝒙 = −𝟐 𝒙 + 𝟑 + 𝟓 17. 𝒇 𝒙 = 𝟏

𝟐𝒙 − 𝟐

vertex: vertex: opens: up down opens: up down narrower wider same width narrower wider same width

Directions: Graph the given function. Then find the key graphical information. 18. 𝒇 𝒙 = − 𝟏

𝟑𝒙 − 𝟐 + 𝟒

Domain: Range: x-intercept(s): y-intercept: relative minimum: relative maximum: intervals of increase: intervals of decrease: 19. 𝒚 = 𝟐 𝒙 + 𝟏 − 𝟑 Domain: Range: x-intercept(s): y-intercept: relative minimum: relative maximum: intervals of increase: intervals of decrease: 20. Give the key information for the given graph. Domain: Range: x-intercept(s): y-intercept: relative minimum: relative maximum: intervals of increase: intervals of decrease:

Algebra 2 Name______________________________ Unit 1: Functions

Assignment 1.3

Make a table and graph each function. Then determine the domain and range. 1. f (x) = −x2 + 2x +3 2. f (x) = −2x − 5

3. f (x) = x + 2 4. f (x) = 2x2

x y

x y

x y

x y

Advanced Algebra 2 Name

ALT01

Worksheet 1 – Graphing Common Functions

For exercises 1-8, make a table (if necessary) and graph each function. For fun, let’s also write the domains and ranges for

each function.

1. y = |x|+ 2 2. y = |x|� 3

x

y

�5 5

�5

5

�10 10

�10

10

x

y

�5 5

�5

5

�10 10

�10

10

Domain: Range: Domain: Range:

3. y = |x+ 2| 4. y = |x� 3|

x

y

�5 5

�5

5

�10 10

�10

10

x

y

�5 5

�5

5

�10 10

�10

10

Domain: Range: Domain: Range:

1 of 2

Advanced Algebra 2 Name

ALT01

Worksheet 1 – Graphing Common Functions

For exercises 1-8, make a table (if necessary) and graph each function. For fun, let’s also write the domains and ranges for

each function.

1. y = |x|+ 2 2. y = |x|� 3

x

y

�5 5

�5

5

�10 10

�10

10

x

y

�5 5

�5

5

�10 10

�10

10

Domain: Range: Domain: Range:

3. y = |x+ 2| 4. y = |x� 3|

x

y

�5 5

�5

5

�10 10

�10

10

x

y

�5 5

�5

5

�10 10

�10

10

Domain: Range: Domain: Range:

1 of 2

Advanced Algebra 2 Name

ALT01

Worksheet 1 – Graphing Common Functions

For exercises 1-8, make a table (if necessary) and graph each function. For fun, let’s also write the domains and ranges for

each function.

1. y = |x|+ 2 2. y = |x|� 3

x

y

�5 5

�5

5

�10 10

�10

10

x

y

�5 5

�5

5

�10 10

�10

10

Domain: Range: Domain: Range:

3. y = |x+ 2| 4. y = |x� 3|

x

y

�5 5

�5

5

�10 10

�10

10

x

y

�5 5

�5

5

�10 10

�10

10

Domain: Range: Domain: Range:

1 of 2

Advanced Algebra 2 Name

ALT01

Worksheet 1 – Graphing Common Functions

For exercises 1-8, make a table (if necessary) and graph each function. For fun, let’s also write the domains and ranges for

each function.

1. y = |x|+ 2 2. y = |x|� 3

x

y

�5 5

�5

5

�10 10

�10

10

x

y

�5 5

�5

5

�10 10

�10

10

Domain: Range: Domain: Range:

3. y = |x+ 2| 4. y = |x� 3|

x

y

�5 5

�5

5

�10 10

�10

10

x

y

�5 5

�5

5

�10 10

�10

10

Domain: Range: Domain: Range:

1 of 2

Algebra 2 Name______________________________ Unit 1: Functions

Assignment 1.3

Make a table and graph each function. Then determine the domain and range. 1. f (x) = −x2 + 2x +3 2. f (x) = −2x − 5

3. f (x) = x + 2 4. f (x) = 2x2

x y

x y

x y

x y

Advanced Algebra 2 Name

ALT01

Worksheet 1 – Graphing Common Functions

For exercises 1-8, make a table (if necessary) and graph each function. For fun, let’s also write the domains and ranges for

each function.

1. y = |x|+ 2 2. y = |x|� 3

x

y

�5 5

�5

5

�10 10

�10

10

x

y

�5 5

�5

5

�10 10

�10

10

Domain: Range: Domain: Range:

3. y = |x+ 2| 4. y = |x� 3|

x

y

�5 5

�5

5

�10 10

�10

10

x

y

�5 5

�5

5

�10 10

�10

10

Domain: Range: Domain: Range:

1 of 2

Advanced Algebra 2 Name

ALT01

Worksheet 1 – Graphing Common Functions

For exercises 1-8, make a table (if necessary) and graph each function. For fun, let’s also write the domains and ranges for

each function.

1. y = |x|+ 2 2. y = |x|� 3

x

y

�5 5

�5

5

�10 10

�10

10

x

y

�5 5

�5

5

�10 10

�10

10

Domain: Range: Domain: Range:

3. y = |x+ 2| 4. y = |x� 3|

x

y

�5 5

�5

5

�10 10

�10

10

x

y

�5 5

�5

5

�10 10

�10

10

Domain: Range: Domain: Range:

1 of 2

Advanced Algebra 2 Name

ALT01

Worksheet 1 – Graphing Common Functions

For exercises 1-8, make a table (if necessary) and graph each function. For fun, let’s also write the domains and ranges for

each function.

1. y = |x|+ 2 2. y = |x|� 3

x

y

�5 5

�5

5

�10 10

�10

10

x

y

�5 5

�5

5

�10 10

�10

10

Domain: Range: Domain: Range:

3. y = |x+ 2| 4. y = |x� 3|

x

y

�5 5

�5

5

�10 10

�10

10

x

y

�5 5

�5

5

�10 10

�10

10

Domain: Range: Domain: Range:

1 of 2

Advanced Algebra 2 Name

ALT01

Worksheet 1 – Graphing Common Functions

For exercises 1-8, make a table (if necessary) and graph each function. For fun, let’s also write the domains and ranges for

each function.

1. y = |x|+ 2 2. y = |x|� 3

x

y

�5 5

�5

5

�10 10

�10

10

x

y

�5 5

�5

5

�10 10

�10

10

Domain: Range: Domain: Range:

3. y = |x+ 2| 4. y = |x� 3|

x

y

�5 5

�5

5

�10 10

�10

10

x

y

�5 5

�5

5

�10 10

�10

10

Domain: Range: Domain: Range:

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