Questions and Answers
What is a relation?
A pairing of numbers in the domain with numbers in the range.
What is the range of a relation?
The output (y).
What is the domain in a relation?
The input (x).
What defines a function?
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What is the Vertical Line Test?
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What does an equation in two variables look like?
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What is a solution to the equation in two variables?
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What is the graph of an equation of two variables?
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What is a linear equation?
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What characterizes a linear function?
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What does function form mean?
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What is the x-intercept?
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What is the y-intercept?
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What is slope?
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What does rise refer to in slope?
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What does run refer to in slope?
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Positive slope means the line rises.
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Negative slope means the line falls.
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Zero slope means the line is horizontal.
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Undefined slope means the line is horizontal.
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What is the Slope-Intercept Form?
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Study Notes
Key Terms in Relations and Functions
- Relation: A pairing of values from the domain (input) with values from the range (output).
- Range: Refers to the set of possible output values (y) from a function.
- Domain: Represents the set of input values (x) for a function.
- Function: A specific type of relation where each input corresponds to exactly one output.
- Vertical Line Test: A graphical method to assess if a relation is a function by checking if any vertical line crosses the graph more than once.
Equations and Solutions
- Equation in Two Variables: An example includes 2x - y = 5, representing a relationship between x and y.
- Solution to the Equation in Two Variables: An ordered pair (x, y) that makes the equation true. For instance, (1, -3) satisfies 2(1) - (-3) = 5.
- Graph of an Equation of Two Variables: The visual representation of all possible solutions on a coordinate plane.
Types of Equations
- Linear Equation: An equation that graphically represents a straight line.
- Linear Function: A specific type of function where the graph is a non-vertical line.
Function Form
- Function Form: When a linear function equation is rearranged to isolate y. For instance, y = -3x + 7 is in function form, while 3x + y = 7 is not.
Intercepts and Slope
- x-intercept: The point where the graph crosses the x-axis, denoting the x-coordinate at that intersection.
- y-intercept: The point where the graph crosses the y-axis, indicating the y-coordinate at that intersection.
- Slope: A measure of the steepness of a line calculated as the ratio of vertical change (rise) to horizontal change (run).
Slope Characteristics
- Rise: Refers to the vertical change in the slope of a line.
- Run: Refers to the horizontal change in the slope of a line.
- Positive Slope: Occurs when the line rises as it moves from left to right.
- Negative Slope: Arises when the line falls from left to right.
- Zero Slope: Describes a horizontal line where there is no vertical change.
- Undefined Slope: Characterizes a vertical line where horizontal change is zero.
Slope-Intercept Form
- Slope-Intercept Form: The linear equation format y = mx + b, where m represents the slope and b denotes the y-intercept.
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Description
Test your understanding of key terms from Sections 8.1 to 8.5 of the Holt McDougal Larson Pre-Algebra textbook. This quiz covers essential vocabulary including relation, range, domain, function, and the vertical line test. Perfect for reinforcing your learning and preparing for assessments.