## Podcast Beta

## Questions and Answers

What is a function?

What is function notation?

A type of writing that uses a letter to name a function and places parentheses around the independent variable.

What is the domain of a function?

The set of all allowable input values.

What is an input in the context of a function?

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What does an input-output diagram show?

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What is the output of a function?

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What is the range of a function?

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What does mapping mean in the context of functions?

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What is a mapping diagram?

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What is a relation in mathematics?

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What does an input-output table display?

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What is an ordered pair?

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What does vertical mean in geometry?

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What is the vertical line test?

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What does horizontal mean in geometry?

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What is the horizontal line test?

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What is a many-to-one function?

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What is a one-to-one function?

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What is an arithmetic sequence?

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What is common difference?

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What is common ratio?

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What is exponential decay?

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What is exponential growth?

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What is a geometric sequence?

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What is a sequence?

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What is the commutative property?

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## Study Notes

### Functions and Relationships

- A function is a relationship where one quantity depends on another, indicating a dependent relationship.
- Function notation uses a letter (e.g., F) followed by parentheses containing the independent variable, pronounced as "F of x."

### Domain and Range

- Domain refers to the complete set of allowable input values, represented by x-values on a graph.
- Range encompasses all output values (y-values) that a function can yield.

### Inputs and Outputs

- Input is the independent variable that is entered into a function.
- Output is the dependent variable, resulting from the function's computation.

### Input-Output Relationship

- Input-output diagrams illustrate the relationship between inputs and outputs using arrows to link them.
- Input-output tables organize inputs in one column and corresponding outputs in another.

### Mappings and Relations

- Mapping connects inputs to outputs, with functional mappings requiring each input to be associated with a single output.
- A relation can map a single input to multiple outputs, differentiating it from a function.

### Graphing and Lines

- Vertical lines run straight up and down; their equation is x = a.
- Horizontal lines run left to right, characterized by the equation y = a.
- The vertical line test determines if a graph is a function by checking for intersections with vertical lines.
- The horizontal line test assesses if a graph is a one-to-one function, meaning each output is paired with one unique input.

### Function Types

- Many-to-one functions occur when multiple x-values correspond to a single y-value.
- One-to-one functions ensure that each output comes from only one input.

### Sequences

- An arithmetic sequence features a consistent difference between consecutive terms.
- The common difference represents the fixed value between terms in an arithmetic sequence.
- A geometric sequence maintains a constant ratio between successive terms, termed common ratio.

### Growth and Decay

- Exponential growth involves a quantity increasing by a consistent ratio over intervals.
- Exponential decay describes a quantity decreasing by a consistent ratio at regular intervals.

### Mathematical Properties

- The commutative property states that the order of addition or multiplication doesn't affect the result: a + b = b + a and ab = ba.

## Studying That Suits You

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## Description

Test your understanding of key terms in Algebra Unit 3 with these flashcards. Each card provides a definition for essential concepts such as functions, function notation, and domain. Perfect for students looking to reinforce their algebra skills.