Types of Functions and Transformations

PARENT FUNCTIONS

TYPES OF PARENT FUNCTIONS

+ TRANSFORMATIONS

05

01

04

03

02

RADICAL

LINEAR

CUBIC

QUADRATIC

ABSOLUTE VALUE

06

09

08

07

TRANSFORMATIONS

Rational (inverse)

EXPONENTIAL

LOGARITHMIC

rational (inverse squared)

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Absolute value

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y=x

Linear function

y= |x|

Quadratic

Linear

Absolute Value

Absolute value

Cubic

quadratic function

y = x2

Radical

Quadratic

CUBIC

y = x3

Rational (Inverse)

Cubic

RADICAL

y = √

Rational (Inverse Squared)

Radical

RATIONAL (INVERSE)

y = 1

Logarithmic

Rational(Inverse)

RATIONAL (INVERSE SQUARED)

y = 1

x2

Rational (Inverse Squared)

Constant

LOGARITHMIC

y = logb (x), b >1Example: y = log2 (x)

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Transformations

Logarithmic

exponential

y = bx, b >1Example: y = 2x

Example

Exponential

Consider the quadratic function y=x2

Transform function 2 units to the right, and 1 unit down:

Function will turn into: y = (x-2)2-1

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