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Questions and Answers
What is the set of all possible inputs of a function?
What is the set of all possible inputs of a function?
What type of function has a constant rate of change?
What type of function has a constant rate of change?
What is the purpose of the distributive property in algebra?
What is the purpose of the distributive property in algebra?
What is the notation f(x) = x^2 an example of?
What is the notation f(x) = x^2 an example of?
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What is the algebraic property that states a + b = b + a?
What is the algebraic property that states a + b = b + a?
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What type of function is of the form f(x) = a^x, where a is a constant?
What type of function is of the form f(x) = a^x, where a is a constant?
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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).
- It is denoted by a letter such as f, g, or h, and is read as "f of x" or "f(x)".
- A function can be thought of as a machine that takes an input (or inputs) and produces a corresponding output.
Key Concepts:
- Domain: The set of all possible inputs (x-values) of a function.
- Range: The set of all possible outputs (y-values) of a function.
- Function notation: A shorthand way of writing functions, e.g., f(x) = x^2.
Types of Functions:
- Linear functions: Functions with a constant rate of change, e.g., f(x) = 2x + 3.
- Quadratic functions: Functions of the form f(x) = ax^2 + bx + c, where a ≠ 0.
- Exponential functions: Functions of the form f(x) = a^x, where a is a constant.
- Polynomial functions: Functions consisting of variables and coefficients combined using only addition, subtraction, and multiplication.
Algebraic Expressions
Simplifying Expressions:
- Combining like terms: Combining terms with the same variable(s) and coefficient(s).
- Distributive property: Expanding products of sums using the rule a(b + c) = ab + ac.
Algebraic Properties:
- Commutative property of addition: a + b = b + a
- Associative property of addition: (a + b) + c = a + (b + c)
- Distributive property: a(b + c) = ab + ac
Functions
- A function is a relation between a set of inputs (domain) and a set of possible outputs (range).
- A function can be thought of as a machine that takes an input (or inputs) and produces a corresponding output.
- Functions are denoted by a letter (e.g. f, g, or h) and are read as "f of x" or "f(x)".
Key Concepts
- Domain: The set of all possible inputs (x-values) of a function.
- Range: The set of all possible outputs (y-values) of a function.
- Function notation: A shorthand way of writing functions, e.g., f(x) = x^2.
Types of Functions
- Linear functions: Functions with a constant rate of change, e.g., f(x) = 2x + 3.
- Quadratic functions: Functions of the form f(x) = ax^2 + bx + c, where a ≠ 0.
- Exponential functions: Functions of the form f(x) = a^x, where a is a constant.
- Polynomial functions: Functions consisting of variables and coefficients combined using only addition, subtraction, and multiplication.
Algebraic Expressions
- Simplifying Expressions: Combining like terms by combining terms with the same variable(s) and coefficient(s).
- Distributive property: Expanding products of sums using the rule a(b + c) = ab + ac.
Algebraic Properties
- Commutative property of addition: a + b = b + a.
- Associative property of addition: (a + b) + c = a + (b + c).
- Distributive property: a(b + c) = ab + ac.
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Description
Learn about the basics of functions, including domain and range, and how they can be thought of as a machine that takes an input and produces a corresponding output.
