Questions and Answers
What is a function?
A special type of relationship in algebra where two quantities are related to each other so that one quantity depends on the other.
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 in a function?
The set of all allowable input values.
What is an input?
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What is an input-output diagram?
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What is output in a function?
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What is the range of a function?
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What does mapping refer to in functions?
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What is a mapping diagram?
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What is a relation?
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What is an input-output table?
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What is a table in the context of functions?
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What is an ordered pair?
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What does vertical mean in a coordinate plane?
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What is the vertical line test?
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What does horizontal mean in a coordinate plane?
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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 a common difference?
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What is a 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 Relations
- A function indicates a relationship where one quantity depends on another, establishing a dependent and independent variable connection.
- Function notation employs a letter designation for the function, using parentheses for the independent variable (e.g., F(x) pronounced "F of x").
- The domain consists of all permissible input values, represented by x-values in a function's graph.
- Input refers to the value entered into a function, represented as the independent variable.
Diagrams and Tables
- An input-output diagram visualizes the connection between inputs and outputs in a function.
- Output signifies the result produced by a function, considered the dependent variable.
- The range encompasses all output values that a function can produce (y-values).
- Mapping represents the structured connection of inputs to outputs; if each input links to only one output, it is classified as a function.
- A mapping diagram illustrates how specific relations pair input values with output values.
- An input-output table lists input values in the first column and corresponding output values in the second, representing domain and range.
- A table is a structured format for displaying data, organized in rows and columns for clarity.
Coordinate Geometry
- An ordered pair, defined in parentheses, indicates a point's location on a coordinate plane, comprising an x and y value.
- Vertical lines run straight up and down on a coordinate plane; their equation takes the form x = a, where 'a' is a constant.
- The vertical line test evaluates if a graph represents a function—if it intersects multiple points with a vertical line, it’s not a function.
- Horizontal lines extend from left to right in a coordinate plane, written as y = a, with 'a' as a constant.
- The horizontal line test checks if a graph is a one-to-one function.
Types of Functions
- A many-to-one function maps multiple x-values to a single y-value.
- A one-to-one function links each y-value to one unique x-value.
Sequences
- An arithmetic sequence maintains a constant difference between consecutive terms.
- The common difference refers to the fixed value separating consecutive numbers in an arithmetic sequence.
- A geometric sequence involves maintaining a consistent ratio between successive terms.
- The common ratio is the consistent multiplier between consecutive numbers in a geometric sequence.
- Exponential growth describes a quantity increasing by a common ratio at regular intervals, while exponential decay refers to a quantity decreasing in the same manner.
- A sequence presents an ordered pattern of numbers, exemplified by decreasing terms such as 11, 7, 3, -1, etc.
Properties of Operations
- The commutative property states that the order of addition or multiplication does not affect the result (e.g., a + b = b + a).
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Description
Test your understanding of functions and relations with this quiz. Dive into concepts such as dependent and independent variables, function notation, domain, and range. Prepare to visualize these connections through diagrams and mappings.
