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Questions and Answers
What parent function is this
What parent function is this
A function is a way of assigning to each input (or element of the ______) exactly one output (or element of the range).
A function is a way of assigning to each input (or element of the ______) exactly one output (or element of the range).
domain
The notation ______(x) is used to indicate the output of the function f when the input is x.
The notation ______(x) is used to indicate the output of the function f when the input is x.
f
A function is one-to-one if each output is associated with only one ______.
A function is one-to-one if each output is associated with only one ______.
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A function is onto if every output is associated with at least one ______.
A function is onto if every output is associated with at least one ______.
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The ______ of two functions f and g, denoted as (f ∘ g)(x), is the function that results from applying g to the input and then applying f to the output.
The ______ of two functions f and g, denoted as (f ∘ g)(x), is the function that results from applying g to the input and then applying f to the output.
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The ______ of a function is a visual representation of the relationship between the input and output.
The ______ of a function is a visual representation of the relationship between the input and output.
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Study Notes
Functions
- A function is a relation between a set of inputs (called the domain) and a set of possible outputs (called the range), assigning each input to exactly one output.
Notation
- Functions are denoted by letters such as f, g, and h.
- The notation f(x) indicates the output of the function f when the input is x.
Types of Functions
One-to-One (Injective) Function
- A function is one-to-one if each output is associated with only one input.
Onto (Surjective) Function
- A function is onto if every output is associated with at least one input.
Bijective Function
- A function is bijective if it is both one-to-one and onto.
Function Operations
Composition
- The composition of two functions f and g, denoted as (f ∘ g)(x), applies g to the input and then applies f to the output.
Inverse
- The inverse of a function f, denoted as f^(-1), reverses the output and input of f.
Graphical Representation
- The graph of a function visually represents the relationship between the input and output.
- The graph determines the domain and range of the function.
Properties of Functions
Domain
- The set of inputs for which the function is defined.
Range
- The set of possible outputs of the function.
Identity
- The identity function, denoted as I, maps each input to itself.
Constant
- A constant function maps every input to a single output.
Function Examples
Linear Function
- A function of the form f(x) = mx + b, where m and b are constants.
Quadratic Function
- A function of the form f(x) = ax^2 + bx + c, where a, b, and c are constants.
Exponential Function
- A function of the form f(x) = a^x, where a is a constant.
Polynomial Function
- A function of the form f(x) = a_n x^n + a_(n-1) x^(n-1) +...+ a_1 x + a_0, where a_n,..., a_0 are constants.
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Description
Learn about the definition and notation of functions, including one-to-one and other types of functions in mathematics.
