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Questions and Answers
What is the domain of the function f(x) = âˆš(x  2)?
Which of the following is a quadratic function?
What is the composition of the functions f(x) = 2x + 1 and g(x) = x^2, denoted as (f âˆ˜ g)(x)?
If f(x) = x^3  2x, is f(x) an even function, an odd function, or neither?
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If f(x) = 3x  2 and g(x) = x + 1, what is the sum of the functions (f + g)(x)?
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Study Notes
Functions
Definition
 A function is a relation between a set of inputs (called the domain) and a set of possible outputs (called the range).
 A function is a way of describing a relationship between variables.
Notation
 Functions are often denoted by letters such as f, g, or h.
 The function notation is f(x) = output, where x is the input.
Domain and Range
 The domain is the set of all possible inputs (xvalues) of a function.
 The range is the set of all possible outputs (yvalues) of a function.
Types of Functions
 Linear Functions: f(x) = mx + b, where m is the slope and b is the yintercept.
 Quadratic Functions: f(x) = ax^2 + bx + c, where a, b, and c are constants.
 Exponential Functions: f(x) = a^x, where a is a constant.
 Polynomial Functions: f(x) = a_nx^n + a_(n1)x^(n1) + ... + a_1x + a_0, where n is a positive integer.
Function Operations
 Addition: (f + g)(x) = f(x) + g(x)
 Subtraction: (f  g)(x) = f(x)  g(x)
 Multiplication: (f Ã— g)(x) = f(x) Ã— g(x)
 Composition: (f âˆ˜ g)(x) = f(g(x))
Graphing Functions
 The graph of a function is a visual representation of the relationship between the input and output.
 The xaxis represents the domain, and the yaxis represents the range.
 The graph can be used to identify key features such as the xintercept, yintercept, and vertex.
Function Properties

Even and Odd Functions:
 Even function: f(x) = f(x)
 Odd function: f(x) = f(x)

Increasing and Decreasing Functions:
 Increasing function: f(x) â‰¤ f(y) if x â‰¤ y
 Decreasing function: f(x) â‰¥ f(y) if x â‰¤ y
Functions
Definition
 A function is a relation between a set of inputs (domain) and a set of possible outputs (range), describing a relationship between variables.
Notation and Basics
 Functions are denoted by letters such as f, g, or h.
 Function notation is f(x) = output, where x is the input.
 Domain is the set of all possible inputs (xvalues) of a function.
 Range is the set of all possible outputs (yvalues) of a function.
Types of Functions
Linear Functions
 f(x) = mx + b, where m is the slope and b is the yintercept.
Quadratic Functions
 f(x) = ax^2 + bx + c, where a, b, and c are constants.
Exponential Functions
 f(x) = a^x, where a is a constant.
Polynomial Functions
 f(x) = a_nx^n + a_(n1)x^(n1) +...+ a_1x + a_0, where n is a positive integer.
Function Operations
 (f + g)(x) = f(x) + g(x) (Addition)
 (f  g)(x) = f(x)  g(x) (Subtraction)
 (f Ã— g)(x) = f(x) Ã— g(x) (Multiplication)
 (f âˆ˜ g)(x) = f(g(x)) (Composition)
Graphing Functions
 Graph of a function is a visual representation of the relationship between input and output.
 xaxis represents the domain, and yaxis represents the range.
 Graph can be used to identify key features such as xintercept, yintercept, and vertex.
Function Properties
Even and Odd Functions
 Even function: f(x) = f(x)
 Odd function: f(x) = f(x)
Increasing and Decreasing Functions
 Increasing function: f(x) â‰¤ f(y) if x â‰¤ y
 Decreasing function: f(x) â‰¥ f(y) if x â‰¤ y
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Description
Understanding functions, notation, domain and range in mathematics. Learn about the definition, notation and important concepts related to functions.