Podcast
Questions and Answers
What is a function?
What is a function?
- A relationship where quantities depend on each other (correct)
- A random set of numbers
- A constant value
- A single number
What is function notation?
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?
What is the domain of a function?
The set of all allowable input values.
What is an input in the context of a function?
What is an input in the context of a function?
What does an input-output diagram show?
What does an input-output diagram show?
What is the output of a function?
What is the output of a function?
What is the range of a function?
What is the range of a function?
What does mapping mean in the context of functions?
What does mapping mean in the context of functions?
What is a mapping diagram?
What is a mapping diagram?
What is a relation in mathematics?
What is a relation in mathematics?
What does an input-output table display?
What does an input-output table display?
What is an ordered pair?
What is an ordered pair?
What does vertical mean in geometry?
What does vertical mean in geometry?
What is the vertical line test?
What is the vertical line test?
What does horizontal mean in geometry?
What does horizontal mean in geometry?
What is the horizontal line test?
What is the horizontal line test?
What is a many-to-one function?
What is a many-to-one function?
What is a one-to-one function?
What is a one-to-one function?
What is an arithmetic sequence?
What is an arithmetic sequence?
What is common difference?
What is common difference?
What is common ratio?
What is common ratio?
What is exponential decay?
What is exponential decay?
What is exponential growth?
What is exponential growth?
What is a geometric sequence?
What is a geometric sequence?
What is a sequence?
What is a sequence?
What is the commutative property?
What is the commutative property?
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.