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Questions and Answers
What is a dependent quantity?
What is a dependent quantity?
What is an independent quantity?
What is an independent quantity?
What is a relation?
What is a relation?
The mapping between a set of input values and a set of output values.
What does the domain of a function represent?
What does the domain of a function represent?
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What is a range in mathematics?
What is a range in mathematics?
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Define a function.
Define a function.
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What is the vertical line test?
What is the vertical line test?
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What does a discrete graph represent?
What does a discrete graph represent?
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What is a continuous graph?
What is a continuous graph?
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What is the purpose of function notation?
What is the purpose of function notation?
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What characterizes an increasing function?
What characterizes an increasing function?
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What is a decreasing function?
What is a decreasing function?
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Define a constant function.
Define a constant function.
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What is a function family?
What is a function family?
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What are linear functions?
What are linear functions?
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Define exponential functions.
Define exponential functions.
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What is an absolute minimum in a function?
What is an absolute minimum in a function?
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What does absolute maximum refer to?
What does absolute maximum refer to?
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What are quadratic functions?
What are quadratic functions?
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Define linear absolute value functions.
Define linear absolute value functions.
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What are linear piecewise functions?
What are linear piecewise functions?
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What is an x-intercept?
What is an x-intercept?
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What is a y-intercept?
What is a y-intercept?
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Study Notes
Key Terms in Algebra 1 Honors
- Dependent Quantity: The variable in a problem that relies on another variable.
- Independent Quantity: The variable that influences the dependent quantity in a problem.
Relations and Their Components
- Relation: A method of pairing input values with corresponding output values.
- Domain: The complete set of input values for a relation.
- Range: The complete set of output values that correspond to the domain.
Functions and Their Properties
- Function: A specific type of relation where each input (from the domain) corresponds to exactly one output (in the range).
- Function Notation: A notation system to express functions algebraically for easy identification of variables.
- Vertical Line Test: A graphical method to determine if a relation is a function by checking if vertical lines intersect the graph at more than one point.
Graph Types
- Discrete Graph: Represents data using distinct, separate points.
- Continuous Graph: Consists of points connected by lines or curves, with no breaks.
Function Behavior
- Increasing Function: A function where the dependent quantity rises as the independent quantity increases over the entire domain.
- Decreasing Function: A function where both the independent and dependent quantities decline through the domain.
- Constant Function: A function that maintains the same output regardless of the independent variable’s value.
Function Families
- Function Family: A collection of functions sharing similar properties.
- Linear Functions: Functions that graph as straight lines.
- Exponential Functions: Functions where the independent variable acts as an exponent.
- Quadratic Functions: Functions characterized by smooth, U-shaped graphs.
- Linear Absolute Value Functions: Functions whose graphs form a V-shape due to the absolute value.
- Linear Piecewise Functions: Functions composed of different linear equations based on specific intervals of the domain.
Important Points on Graphs
- Absolute Minimum: The lowest point in the graph, marked by the least y-coordinate.
- Absolute Maximum: The highest point in the graph, characterized by the greatest y-coordinate.
- X-Intercept: The point at which the graph intersects the x-axis.
- Y-Intercept: The point at which the graph intersects the y-axis.
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Description
This quiz focuses on essential vocabulary definitions from Algebra 1 Honors Module 1. Key terms such as 'dependent quantity,' 'independent quantity,' 'relation,' and 'domain' are included to help you understand core concepts in algebra. Enhance your vocabulary and comprehension with these flashcards!