Algebra 2: Unit 1
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: |
| | | |
| | | |
| | | |
| | | |
| | |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
-----------------------
-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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