Questions and Answers
What is a dependent variable?
The variable in a relation with a value that depends on the value of the independent variable.
What is a function?
A relationship between input and output where there is exactly one output for each input.
What is an independent variable?
The value of the variable in a relation that determines the output.
What is a linear equation?
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What is a linear function?
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What is the vertical line test?
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What is another name for the coordinate plane?
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What is a domain in mathematics?
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What is an ordered pair?
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What is the origin in a coordinate system?
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What is a range in mathematics?
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What is a relation?
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What is the x-axis?
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What is the y-axis?
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What is mapping in mathematics?
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What is a discrete function?
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What is a continuous function?
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What is function notation?
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What is a nonlinear function?
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What is an exponential function?
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What is a parabola?
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What is a quadratic function?
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Study Notes
Key Concepts in Relations, Functions, and Graphing
- Dependent Variable: Its value is influenced by the independent variable in a relation.
- Function: A specific type of relation; each input is associated with exactly one output.
- Independent Variable: The variable that determines the output’s value in a functions’ relation.
Types of Equations and Functions
- Linear Equation: Contains variables without exponents other than 1; graphs to a straight line.
- Linear Function: A function whose graph results in a straight line, representing a constant rate of change.
- Nonlinear Function: A function whose graph does not form a straight line, indicating a variable rate of change.
Graphing Essentials
- Vertical Line Test: A method to verify if a relation is a function; any vertical line should intersect the graph at most once per x-value.
- Coordinate Plane: The grid where points are plotted, formed by intersecting horizontal (x-axis) and vertical (y-axis) number lines.
- Ordered Pair: A coordinate representation in the form (x, y), indicating a point's position on the plane.
Components of Functions
- Domain: The complete set of x-coordinates (input values) from all ordered pairs in a function.
- Range: The complete set of y-coordinates (output values) derived from the range of the independent variable.
- Origin: The central point (0,0) on the coordinate plane where the x-axis and y-axis intersect.
Types of Functions
- Discrete Function: Represented by separate points; the graph does not connect them.
- Continuous Function: Illustrated by a smooth line or curve; indicates a complete range of values.
- Exponential Function: Function expressed as y = a^x, where a is a positive constant not equal to one.
- Quadratic Function: Defined by the form y = ax² + bx + c, with the coefficient 'a' being non-zero.
Additional Concepts
- Function Notation: A way to denote functions using symbols, such as f(x) = 3x - 8.
- Mapping: A visual representation showing how each value in the domain relates to a value in the range.
- Parabola: The graphical representation of quadratic functions typically U-shaped.
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Test your understanding of key concepts in relations, functions, and graphing with these flashcards. Each card defines important terms you'll encounter in Chapter 3 of Algebra I. Perfect for quick reviews before exams!