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Questions and Answers
What is the definition of a relation?
What is the definition of a relation?
What is the domain of a relation?
What is the domain of a relation?
What is the characteristic of a one-to-one function?
What is the characteristic of a one-to-one function?
What is the result of applying one function to the output of another function?
What is the result of applying one function to the output of another function?
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What is an onto function?
What is an onto function?
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How can a function be represented?
How can a function be represented?
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What is the characteristic of an even function?
What is the characteristic of an even function?
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What is the range of a relation?
What is the range of a relation?
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What is the purpose of an inverse function?
What is the purpose of an inverse function?
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What is the difference between a relation and a function?
What is the difference between a relation and a function?
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Study Notes
Relations and Functions
Relations
- A relation is a set of ordered pairs.
- It can be represented as:
- A set of ordered pairs: {(a, b), (c, d), ...}
- A table or matrix
- A graph on a coordinate plane
- The domain of a relation is the set of all first elements (x-coordinates) in the ordered pairs.
- The range of a relation is the set of all second elements (y-coordinates) in the ordered pairs.
Functions
- A function is a relation in which every element in the domain corresponds to exactly one element in the range.
- It can be represented as:
- A set of ordered pairs: {(a, b), (c, d), ...}
- A table or matrix
- A graph on a coordinate plane
- The domain of a function is the set of all input values (x-coordinates) in the ordered pairs.
- The range of a function is the set of all output values (y-coordinates) in the ordered pairs.
- A function can be represented algebraically using a formula, such as f(x) = x^2 + 3x - 4.
Characteristics of Functions
- Domain: The set of input values for which the function is defined.
- Range: The set of output values of the function.
- One-to-one: A function is one-to-one if each element in the range corresponds to exactly one element in the domain.
- Onto: A function is onto if every element in the range is the output of at least one element in the domain.
Operations with Functions
- Function Composition: The result of applying one function to the output of another function.
- Inverse Functions: A function that "reverses" the operation of another function.
- Even and Odd Functions: A function is even if f(-x) = f(x) and odd if f(-x) = -f(x).
Relations and Functions
Relations
- A relation is a set of ordered pairs, which can be represented in different ways, including a set of ordered pairs, a table or matrix, or a graph on a coordinate plane.
- The domain of a relation is the set of all first elements (x-coordinates) in the ordered pairs.
- The range of a relation is the set of all second elements (y-coordinates) in the ordered pairs.
Functions
- A function is a special type of relation in which every element in the domain corresponds to exactly one element in the range.
- A function can be represented in various ways, including a set of ordered pairs, a table or matrix, or a graph on a coordinate plane.
- The domain of a function is the set of all input values (x-coordinates) in the ordered pairs.
- The range of a function is the set of all output values (y-coordinates) in the ordered pairs.
- A function can be represented algebraically using a formula, such as f(x) = x^2 + 3x - 4.
Characteristics of Functions
Domain and Range
- The domain of a function is the set of input values for which the function is defined.
- The range of a function is the set of output values of the function.
One-to-One and Onto Functions
- A function is one-to-one if each element in the range corresponds to exactly one element in the domain.
- A function is onto if every element in the range is the output of at least one element in the domain.
Operations with Functions
Function Composition
- Function composition is the result of applying one function to the output of another function.
Inverse Functions
- An inverse function is a function that "reverses" the operation of another function.
Even and Odd Functions
- A function is even if f(-x) = f(x).
- A function is odd if f(-x) = -f(x).
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Description
This quiz covers the basics of relations and functions, including their representation, domain, and range. Learn about the differences between relations and functions.
