Upload
tracy-roger-eaton
View
227
Download
1
Embed Size (px)
Citation preview
04/19/23 3-4: Parent Functions 1
Parent Functions
Unit 1
04/19/23 3-4: Parent Functions 2
What is a parent function?
The parent function is the simplest function with the defining characteristics of the family. Functions in the same family are transformations of their parent function.
04/19/23 3-4: Parent Functions 3
Algebra Aerobics
04/19/23 3-4: Parent Functions 4
Types of FunctionsFamily
Rule
Graph
Domain
Range
Zeros
Symmetry
Linearf(x) = x
All Real Numbers(–∞, ∞)
All Real Numbers(–∞, ∞)
Constantf(x) = c
All Real Numbers(–∞, ∞)
c
Noney-axis
(0, 0)Origin
Family
Rule
Graph
Domain
Range
Zeros
Symmetry
04/19/23
3-4: Parent Functions 5
Types of FunctionsCubic
f(x) = x3
All Real Numbers(–∞, ∞)
All Real Numbers(–∞, ∞)
Quadraticf(x) = x2
All Real Numbers(–∞, ∞) y > 0
[0, ∞) (0, 0)y-axis
(0, 0)Origin
04/19/23 3-4: Parent Functions 6
Types of FunctionsCubic Root
f(x) = .
All Real Numbers(–∞, ∞)
All Real Numbers(–∞, ∞)
Square Rootf(x) = .
x > 0[0, ∞) y > 0
[0, ∞)
Family
Rule
Graph
Domain
Range
Zeros
Symmetry
x
(0, 0)None
(0, 0)Origin
3 x
04/19/23 3-4: Parent Functions 7
Types of FunctionsAbsolute Value
f(x) = |x|
All Real Numbers(–∞, ∞) y > 0
[0, ∞)
Rationalf(x) = .
All Reals except 0(–∞, 0), (0, –∞)
All Reals except 0(–∞, 0), (0, –∞)
Family
Rule
Graph
Domain
Range
Zeros
Symmetry
1
x
NoneOrigin
(0, 0)y-axis
04/19/23 3-4: Parent Functions 8
Types of FunctionsExponential
f(x) = 2x
All Real Numbers(–∞, ∞) y > 0
[0, ∞)
Logarithmicf(x) = log x
x > 0[0, ∞)
All Real Numbers(–∞, ∞)
Family
Rule
Graph
Domain
Range
Zeros
Symmetry
NoneNone
NoneNone
04/19/23 3-4: Parent Functions 9
Translations
Show with your hands
04/19/23 3-4: Parent Functions 10
f(x) = x – 3
Linear, Down 3
04/19/23 3-4: Parent Functions 11
f(x) = x + 3
Linear, Up 3
04/19/23 3-4: Parent Functions 12
f(x) = 2x
Linear, Steeper by 2
04/19/23 3-4: Parent Functions 13
f(x) = 2x2
Shrinks with a scale of 2
04/19/23 3-4: Parent Functions 14
f(x) = 2x2 – 4
Quadratic Function, Shrinks scale of 2 and
Down 4
04/19/23 3-4: Parent Functions 15
f(x) = x3 + 2
Cubic, Up 2
04/19/23 3-4: Parent Functions 16
f(x) = (–x)2
Quadratic, Reflection
04/19/23 3-4: Parent Functions 17
f(x) = .
Square root, Shrinks by a scale of 3 and down by 4
3 4x
04/19/23 3-4: Parent Functions 18
Moves to the right by 2 and grows horizontally by a scale of 3
04/19/23 3-4: Parent Functions 19
Parent Functions ExamplesIdentify the parent function for g from its function rule. Then,
describe what transformation of the parent function it represents.
1. g(x) = x – 3
2. g(x) = 2x2
3. g(x) = x3 + 2
4. g(x) = (–x)2
5. g(x) =
6.
3 4x
Linear, Down 3
Quadratic, Shrinks with a scale of 2
Cubic, Up 2
Quadratic, Reflection
Square root, Shrinks by a scale of 3 and down by 4
Moves to the right by 2 and grows horizontally by a scale of 3
Parent Function Handout
• Work on Parent Function Handout Questions. This is a daily grade.
04/19/23 3-4: Parent Functions 20