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.
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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.