Algebra 2: Unit 1 - wsfcs.k12.nc.us



Algebra 2: Unit 1

GRAPHING FUNCTIONS and TRANSFORMATIONS

• The original function f(x) is often called the __________________ function.

• We will discuss 3 basic ways to transform the shape of a parent function’s graph.

1) Vertical Translation (Shift): Graph is moved __________________________________

2) Horizontal Translation (Shift): Graph is moved ______________________________________

3) Vertical Dilations, Contractions, and Reflections:

In the vertical direction, ______________________________________________________________

Identify the points of the given parent function f(x) in the graph:

• Graph each transformation of the parent function and describe the change from the original.

• Remember in function notation, f(x) is like the y value of a point so (x, y) (( (x, f(x))

|x |y or f(x) |

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Identify the points of the given parent function g(x) in the graph:

• Graph each transformation of the parent function and describe the change from the original.

For each function, graph the indicated change and write a function statement.

Algebra 2: Unit 1

General Form for Describing the TRANSOFMRATIONS for a function f(x):

F(x) ( a•f(x – h) + k

|“h” |“k” |“a” |

|RIGHT: |DOWN: |SHRINK: |

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| | | |

| | | |

| | | |

| | |STRETCH: |

|LEFT: |UP: | |

| | | |

| | | |

| | | |

| | | |

| | |REFLECT: |

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DESCRIBE THE TRANSFORMATIONS FOR THE GIVEN EXPRESSIONS

For parent functions f(x), g(x), or h(x)

1) f(x – 1) + 2

2) h(x + 7) + 8

3) 2f(x – 1)

4) -3 f(x) + 2

5) ½ g(x) – 9

6) -3/4h(x + 6)

7) 2f(x + 3) – 5

8) –g(x – 4) + 7

9) 2/3h(x + 1) + 5

SPECIFIC FUNCTIONS AND THEIR TRANSFORMATIONS

ABSOLUTE VALUE:

• Parent Function:

f(x) = |x|

• Transformation Function:

a|x – h| + k

• Important Point: (h, k)

• Generic Shape:

• DOMAIN:

•

• RANGE:

• CALCULATOR: [MATH] (_NUM_ ( “1:abs(”

QUADRATIC:

• Parent Function:

f(x) = x2

• Transformation Function:

a(x – h)2 + k

• Important Point: (h, k)

• Generic Shape:

• DOMAIN:

• RANGE:

•

Algebra 2: Unit 1 – Quadratic and Absolute Transformations

PRACTICE SHIFTS WITH ABSOLUTE AND QUADRATIC FUNCTIONS

Section 1: Graph and Identify DOMAIN and RANGE

1) [pic]

[pic]

Domain: ___________________

Range: ______________________

2) [pic]

[pic]

Domain: ___________________

Range: ______________________

[pic]

[pic]

Domain: ___________________

Range: ______________________

3) [pic]

[pic]

Domain: ___________________

Range: ______________________

4) [pic]

[pic]

Domain: ___________________

Range: ______________________

5) [pic]

[pic]

Domain: ___________________

Range: ______________________

6) [pic]

[pic]

Domain: ___________________

Range: ______________________

7) [pic]

[pic]

Domain: ___________________

Range: ______________________

8) [pic]

[pic]

Domain: ___________________

Range: ______________________

Algebra 2: Unit 1 – Quadratic and Absolute Transformations

Section 2: Based on each function statement describe the transformations from the parent function.

1) [pic]

Parent Function: _______________ Transformation: _______________________________________

2) [pic]

Parent Function: _______________ Transformation: _______________________________________

3) [pic]

Parent Function: _______________ Transformation: _______________________________________

4) [pic]

Parent Function: _______________ Transformation: _______________________________________

5) [pic]

Parent Function: _______________ Transformation: _______________________________________

6) [pic]

Parent Function: _______________ Transformation: _______________________________________

7) [pic]

Parent Function: _______________ Transformation: _______________________________________

8) [pic]

Parent Function: _______________ Transformation: ______________________________________

9) [pic]

Parent Function: _______________ Transformation: _______________________________________

10) [pic]

Parent Function: _______________ Transformation: _______________________________________

Section 3: Write the EQUATIONS for described shifts and parent function.

1) Absolute Value; Up 7 and Left 3

1. ______________________________________

2) Quadratic; Reflects and Right 9

2. ______________________________________

3) Absolute Value; Down 4 and Right 1

3. ______________________________________

4) Quadratic; Down 2, Reflects, Vertical shrink of 1/6

4. ______________________________________

5) Absolute Value; Right 6, Vertical stretch of 2

5. ______________________________________

6) Absolute Value; Right 9 and Down 2

6. ______________________________________

7) Quadratic; Vertical Shrink of ½ and Up 3

7. ______________________________________

8) Absolute Value; Left 6 and Reflects

8. ______________________________________

9) Quadratic; Down 6, Vertical Stretch of 5, Right 4

9. ______________________________________

10) Absolute Value; Reflects, Up 2 and Left 9

10. ______________________________________

Algebra 2: Unit 1 – Square Root and Cubic Transformations

SQUARE ROOT:

• Parent Function: [pic]

• Transformation Function:

[pic]

• Important Point: (h, k)

• Generic Shape:

• DOMAIN:

• RANGE:

CUBIC:

• Parent Function: f(x) = x3

• Transformation Function:

a(x – h)3 + k

• Important Point: (h, k)

• Generic Shape:

• DOMAIN:

• RANGE:

PRACTICE SHIFTS WITH CUBE AND SQUARE ROOT FUNCTIONS

Section 1: Graph and Identify DOMAIN and RANGE

1) [pic]

Domain: ______________ Range: ______________

2) [pic]

Domain: ______________ Range: ______________

3) [pic]

Domain: ______________ Range: ______________

4) [pic]

Domain: ______________ Range: ______________

5)

6) [pic]

Domain: ______________ Range: ______________

7) [pic]

Domain: ______________ Range: ______________

8) [pic]

Domain: ______________ Range: ______________

9) [pic]

Domain: ______________ Range: ______________

10) [pic]

Domain: ______________ Range: ______________

11) [pic]

Domain: ______________ Range: ______________

Section 2: Based on each function statement describe the transformations from the parent.

11) [pic]

1) [pic]

2) [pic]

3) [pic]

4) [pic]

5) [pic]

6) [pic]

7) [pic]

8) [pic]

9) [pic]

Section 3: Write the EQUATIONS with described shifts and given parent functions.

1) [pic]; Down 4 and Right 2 1. _____________________________

2) y = x3; Reflects and Right 3 2. _____________________________

3) [pic]; Vertical Shrink 2/5, Left 7 3. _____________________________

4) y = x3; Down 2, Reflects, Vertical Stretch 4 4. _____________________________

5) [pic]; Reflect, Vertical stretch of 3, Up 6 5. _____________________________

6) y = x3; Vertical Shrink 2/3, Left 9 6. _____________________________

7) [pic]; Vertical Stretch 5, Down 7, Right 3 7. _____________________________

8) y = x3; Vertical Shrink of ½, Left 2, Up 8 8. _____________________________

GENERAL PRACTICE:

PART 1: For each of the given graphs, write the EQUATION that would create that graph.

• Graphs are approximately drawn to scale

• There are NO Vertical Shrinks or Stretches from the parent function.

• Focus on the important point of each function based on its parent function.

Section 2: (1) Graph the transformation (2) Label 3 points guaranteed to be on the graph

1) [pic]

2) [pic]

3) [pic]

4) [pic]

5) [pic]

6) [pic]

Section 2a: Identify the DOMAIN and RANGE for each graph:

Section 3: Identify the transformations of each listed function and name the parent function

1) [pic]

2) [pic]

3) [pic]

4) [pic]

5) [pic]

6) [pic]

7) [pic]

8) [pic]

9) [pic]

10) [pic]

Section 4: Write the equation from the given parent function and transformations

• List the coordinate for the new “important point” after transformation

1) Quadratic; Up 3 and Left 7

2) Absolute; Reflects and Right 2

3) Cube; Down 4 and Right 1

4) Square Root; Down 2, Reflects, Shrink 1/6

5) Cube; Right 6, Stretch 2

6) Cube; Left 1, Up 1, Stretch of 4/3

7) Absolute; Right 9 and Down 2

8) Square Root; Vertical 2, Right 3, Up 2

9) Square Root; Vertical 2, Left 2, Down 3

10) Cube; Down 6, Stretch of 5, Right 4

11) Absolute; Reflects, Up 2 and Left 9

12) Quadratic; Shrink 3/4, Down 2

13) Quadratic; Reflects, Stretch 4/3, Left 2

14) Square Root; Right 1 and Up 3

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-1•f(x)

2•f(x)

f(x – 2)

½•f(x)

f(x) – 2

f(x) + 3

f(x)

f(x + 1)

g(x)

g(x) – 4

g(x) + 1

g(x + 3)

g(x – 3)

g(x + 1)

3•g(x)

-2•g(x)

½•g(x)

Shift Up 3

Shift Left 2

f(x)

Vertical Stretch of 3

Reflection

g(x)

Shift Right 3

Shift down 5

h(x)

|x |y or f(x) |

|-2 | |

|-1 | |

|0 | |

|1 | |

|2 | |

|x |y or f(x) |

|-2 | |

|-1 | |

|0 | |

|1 | |

|2 | |

|x |y |

|0 | |

|1 | |

|4 | |

|9 | |

|x |y |

|-2 | |

|-1 | |

|0 | |

|1 | |

|2 | |

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