Questions and Answers
What is a function?
A type of relation where each element in the domain corresponds with exactly one element in the range.
What are the different ways in which functions may be represented?
How do we find an optimal solution to a linear programming problem?
What is the meaning of the domain and range of a function?
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What is the effect of a transformation of an independent variable specifically related to absolute value functions?
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What is the effect of a transformation of a dependent variable for absolute value functions?
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How can functions be used to model real world situations, make predictions, and solve problems?
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What is the definition of an absolute value function?
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What is a constraint in relation to functions?
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What is a dependent variable?
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What is the domain in relation to a function?
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What is the definition of an equivalent equation and inequality?
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What is a feasible region?
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What is function notation?
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What is a greatest integer function?
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What are the horizontal and vertical axes?
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What is a horizontal translation/shift?
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What is an independent variable?
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What is an inequality?
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What are the input and output of a function?
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What is linear growth?
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What is the maximum/minimum in relation to functions?
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What is an objective function?
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What is a one-to-one function?
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What is optimization?
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What is an ordered pair?
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What is the origin on the coordinate plane?
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What is a parent function?
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What is a piecewise function?
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What is the range of a function?
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What is a relation in mathematics?
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What is a restricted domain?
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What is shading in the context of graphing?
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What is the solution of a system of linear equations?
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What is the solution of a system of linear inequalities?
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What is standard form in mathematics?
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What is slope in mathematics?
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Study Notes
Functions
- A function is a relation where each element in the domain corresponds to one element in the range.
- Functions are represented as f(x) where f(x) equals a mathematical expression, e.g., f(x) = 6x + 7.
Representation of Functions
- Functions can be represented graphically, analytically (equations), or numerically (tables).
Optimal Solutions in Linear Programming
- Optimal solutions are found by identifying the best outcome (maximum or minimum) that satisfies constraints.
Domain and Range
- The domain is the set of possible input values (independent variable).
- The range is the set of possible output values (dependent variable).
Transformations of Absolute Value Functions
- Independent variable transformations affect the input, shifting the graph horizontally.
- Dependent variable transformations affect the output, altering the vertical position of the graph.
Real-World Applications
- Functions model real-world situations, allowing predictions and solutions to various problems.
Absolute Value Function
- A specific type of function representing the distance from zero on the number line.
Constraints
- Constraints are equations or inequalities that define boundaries on the coordinate plane, creating a feasible region.
Dependent Variable
- The dependent variable relies on the independent variable and is plotted on the y-axis.
Independent Variable
- The independent variable is the input value, plotted on the x-axis, and can vary freely.
Feasible Region
- The feasible region is determined by the intersections of inequalities, representing all possible solutions.
One-to-One Function
- A one-to-one function means that each output corresponds uniquely to one input.
Objective Function
- The objective function represents the quantity to be maximized or minimized in optimization problems.
Piecewise Function
- A piecewise function consists of multiple sub-functions for different intervals of its domain.
Ordered Pair
- An ordered pair is a coordinate point in the form (x, y) on the coordinate plane.
Origin
- The origin is the point (0, 0) where the x-axis and y-axis intersect.
Range
- The range consists of output values from a function, typically represented as y-values influenced by x-values of the domain.
Slope
- The slope is defined as the ratio of the rise (change in y) over the run (change in x), indicating the steepness of a line.
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Description
This quiz focuses on the foundational concepts of functions as part of the Algebra 2 Honors curriculum. It covers definitions, representations, and examples essential for understanding functions. Use these flashcards to test your knowledge and prepare for further studies in algebra.
