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Parent Functions

Unit 1

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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.

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Algebra Aerobics

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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

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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

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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

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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

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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

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Translations

Show with your hands

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f(x) = x – 3

Linear, Down 3

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f(x) = x + 3

Linear, Up 3

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f(x) = 2x

Linear, Steeper by 2

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f(x) = 2x2

Shrinks with a scale of 2

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f(x) = 2x2 – 4

Quadratic Function, Shrinks scale of 2 and

Down 4

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f(x) = x3 + 2

Cubic, Up 2

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f(x) = (–x)2

Quadratic, Reflection

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f(x) = .

Square root, Shrinks by a scale of 3 and down by 4

3 4x

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Moves to the right by 2 and grows horizontally by a scale of 3

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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.

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