# Unit 16: Parameter Changes and Parent Functions

```Name:
Period
PreAP
UNIT 16: PARAMETER CHANGES AND PARENT FUNCTIONS
I can define, identify and illustrate the following terms:
Parent Function
Domain
Range
Cubic Function
Absolute Value
Function
Linear Function
Square Root Function
Reciprocal (Rational)
Function
Vertical Stretch
Vertical Compress
Vertical Shift
Horizontal Shift
Reflection
Translation
Parameter Changes
Dates, assignments, and quizzes subject to change without advance notice.
24
Intro Parent Functions
27
HOLIDAY
28
Practice Parent Functions
3
QUIZ
4
Review
29/30
31
Quiz: Parent Functions
Find Domain and Range
Parameter Changes
Write the equation
5, 6 and 7
Test #16: Parameter Changes and Parent Functions
Friday, 5/24
Identify Parent Functions
 I can identify the parent functions for linear, quadratic, cubic, absolute value, square root, and rational functions.
 I can match the parent function graph, to the equation, and give the domain and range.
 I can determine the parent function of a given equation or graph
PRACTICE: Parent Function Day 1
Tuesday, 5/28
Identify Parent Functions
 I can identify the parent functions for linear, quadratic, cubic, absolute value, square root, and rational functions.
 I can match the parent function graph, to the equation, and give the domain and range.
 I can determine the parent function of a given equation or graph
PRACTICE: Parent Function Day 2
Block, 5/29-30
Parameter Changes
 I can describe the transformations from a parent function given an equation.
 I can write the equation given the parent function and the parameter changes
PRACTICE: Parameter Changes Day 1
Friday, 5/31
New Domain and Range
 I can find the new domain and range after parameter changes.
PRACTICE: Parameter Changes Day 2
Monday, 6/3
Quiz
PRACTICE: Quiz and Parameter Change Day 3
Tuesday, 6/4
Review
PRACTICE: Review
Block day and Friday, 6/5, 6, 7
 Test 16: Parameter Changes and Parent Functions
Score:
Parent Function Day 1 Practice
True or False. If it false, then correct the underlined word(s) to make the statement true.
1. The linear parent function is y = x3
2. The quadratic parent function’s range is all real numbers.
3. The cubic parent function’s graph lies only in Quadrant I.
4. The reciprocal parent function’s graph lies only in Quadrants I and III.
1
5. The rational parent function is 𝑦 = 𝑥
For each function, tell the name and equation of the parent function.
6. 𝑦 = (𝑥 − 1)3
7. 𝑦 = (𝑥 + 1)2
8. 𝑦 = −𝑥
9. 𝑦 = √𝑥 + 3
12. 𝑦 =
−1
𝑥
+5
3
15. 𝑦 = − 5 |𝑥| − 2
10. 𝑦 = |𝑥 + 4|
2
13. 𝑦 = 3 𝑥
2
16. 𝑦 = − 3 𝑥 3
1
11. 𝑦 = 𝑥+2
14. 𝑦 = −(𝑥 − 2)2
5
17. 𝑦 = 𝑥
Graph each set of points and then graph the parent function and write the parent function’s equation.
18.
21.
19.
20.
Parent Functions Day 2 Practice
I. Fill in the missing information for each parent function. (Can you do it without looking?)
1
2
3
Name: _____________
Name: _____________
Name: _____________
Equation: _________
Equation: _________
Equation: _________
Domain:___________
Domain:___________
Domain:___________
Range: ____________
Range: ____________
Range: ____________
4
5
6
Name: _____________
Name: _____________
Name: _____________
Equation: _________
Equation: _________
Equation: _________
Domain:___________
Domain:___________
Domain:___________
Range: ____________
Range: ____________
Range: ____________
II. For each function, identify and sketch the parent function.
7
8
9
10
11
12
Square Root
Examples: Identify the parent function and then describe the transformation
1. y  5x3  3
2. y  x  4
3. y  x 2  2
PF:________________
PF:________________
PF:________________
Transformations:
Transformations:
Transformations:
4. y  2 x  4
5. y   x  4  3
1
2
6. y   5 x  3  2
PF:________________
PF:________________
PF:________________
Transformations:
Transformations:
Transformations:
7. y  2  x  3
8. y 
3
1
3
x4
2
3
x
9. y    5
PF:________________
PF:________________
PF:________________
Transformations:
Transformations:
Transformations:
Parameter Changes Day 1 Practice
1. g(x) = x 2 – 1
2. f(x) = 2 x 1
3. h(x) =
PF:________________
PF:________________
PF:________________
Transformations:
Transformations:
Transformations:
4. g(x) = x3+ 3
5. g(x) =
PF:________________
PF:________________
PF:________________
Transformations:
Transformations:
Transformations:
1
x 6
6. f(x) =
x2
1
x  5 -2
4
1
5
x
8. f(x) = -3x + 5
9. f(x) =  x  8
PF:________________
PF:________________
PF:________________
Transformations:
Transformations:
Transformations:
10.
11.
12
PF:________________
PF:________________
PF:________________
Transformations:
Transformations:
Transformations:
13.
14.
15.
PF:________________
PF:________________
PF:________________
Transformations:
Transformations:
Transformations:
7. h(x) =
Examples: Writing Equations from descriptions and New Domain and Range
From a graph, write the equation and the new domain and range.
From an equation, write the new domain and range:
y
x5
g(x) = 3(x-1)2 – 6
g(x) =
1
x 6
Given the parent function and a description, write the equation:
Linear---vertical stretch of 8 and translated up 2.
Rational ---reflected over the x axis, translated down 3
Cubic—translated left 1 and up 9.
Parameter Changes Day 2 Practice
Identify the domain and range of the function. Describe the transformation from its parent function.
1. g(x) = 3 x
Domain : _____________________ Range : ___________________
Transformation:_____________________________________________
2. h(x) = - x2 + 1
Domain : _____________________ Range : ___________________
Transformation:_____________________________________________
3. h(x) =  x  2
Domain : _____________________ Range : ___________________
Transformation:_____________________________________________
4. f(x) =
3
4
x
Domain : _____________________ Range : ___________________
Transformation:_____________________________________________
5. h(x) = 6 (x + 9)2
Domain : _____________________ Range : ___________________
Transformation:_____________________________________________
Given the parent function and a description of the transformation, write the equation of the transformed
function, f(x).
6. Absolute value—vertical shift up 5, horizontal shift right 3.
7. Square root—vertical compression by
____________________
2
5
____________________
8. Cubic—reflected over the x axis and vertical shift down 2
9. Reciprocal—vertical stretch by 8
____________________
____________________
10. Quadratic—vertical compression by .45, horizontal shift left 8.
11. Which graph best represents the function f(x) = 2x2 - 2?
a.
b.
c.
____________________
________________
d.
For each graph: Identify the parent function, write the new domain and range, and write the new equation
12
13
14
15
16
17
Parameter Changes Day 3 Practice
# 1- 7
Give the name of the parent function and describe the transformation represented.
1. g(x) = x 2 – 1
Name: ______________________________
Transformation:_______________________
Domain : _____________________
Range : ___________________
2. f(x) = 2 x 1
Name: ______________________________
Transformation:_______________________
Domain : _____________________
Range : ___________________
3. h(x) =
x2
Name: ______________________________
Transformation:_______________________
Domain : _____________________
Range : ___________________
4. g(x) = x3+ 3
Name: ______________________________
Transformation:________________________
Domain : _____________________
Range : ___________________
5. g(x) = 2(x-3)2 + 1 Name: ______________________________
Transformation:_______________________
Domain : _____________________
Range : ___________________
6. f(x) = x  5 -2
Name: ______________________________
Transformation:_______________________
Domain : _____________________
Range : ___________________
7. h(x) = - &frac12; x + 7
Name: _____________________________
Transformation:______________________
Domain : _____________________
Range : ___________________
8. g(x) = 3 x
Name: _____________________________
Transformation:______________________
Domain : _____________________
Range : ___________________
9. h(x) = - x2 + 1
Name: _____________________________
Transformation:______________________
Domain : _____________________
Range : ___________________
10. h(x) =  x  2
Name: _____________________________
Transformation:______________________
Domain : _____________________
Range : ___________________
Given the parent function and a description of the transformation, write the equation of the transformed
function, f(x).
11. Absolute value—vertical shift up 5, horizontal shift right 3.
12. Square Roots—vertical compression by
2
5
13. Cubic—reflected over the x axis and vertical shift down 2
____________________
____________________
____________________
_________________
REVIEW
Identify the name, equation, domain, and range for each graph.
1.
2.
3.
Name: _________________
Equation: _______________
Domain: _____________
Range: ______________
Name: ___________________
Equation: ________________
Domain: _____________
Range: ______________
Name: ___________________
Equation: ________________
Domain: _____________
Range: ______________
4.
5.
6.
Name: _________________
Equation: _______________
Domain: _____________
Range: ______________
Name: ___________________
Equation: ________________
Domain: _____________
Range: ______________
Name: ___________________
Equation: ________________
Domain: _____________
Range: ______________
Give the name, equation and sketch the graph of the parent function
name______________
equation____________
name______________
equation____________
9) Describe the effect the a, h, and k have a on the graph of the parent function. How do you tell the difference
between a, h, &amp; k?
_______________________________________________________________________
_______________________________________________________________________
_______________________________________________________________________
10) y  2 x  3
11) y   x  2   1
12) y  x  4  3
Parent Function:
Parent Function:
Parent Function:
Transformation:
Transformation:
Transformation:
Domain:
Domain:
Domain:
Range:
Range:
Range:
13) y 
1
3
 x  2  1
2
2
14) y 
1
2
( x  1)
15)
y    x  2 1
Parent Function:
Parent Function:
Parent Function:
Transformation:
Transformation:
Transformation:
Domain:
Domain:
Domain:
Range:
Range:
Range:
2
Write the equation from the graph. Define the Domain and Range.
16)
17)
18)
_______________________
_________________________
_______________________
_______________________
_________________________
_______________________
_______________________
_________________________
_______________________
Write the parent function given the specific conditions
19) Cubic: reflected across the x-axis, translated 3 units up and 13 units left.
__________________
20) Reciprocal: Vertically compressed by 3/4, translated 5 units down.
__________________
21) Quadratic: Vertically stretched by 3, reflected across the x-axis, translated 6 units right.
__________________
22) Square root: Vertically compressed &frac12; , translated 24 units down.
__________________
23) Absolute value: Vertically Stretched by 71, translated 3 units down and 18 units right.
__________________
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