Questions and Answers
Is a function a set of ordered pairs where each input has exactly one output?
Not a function implies that at least one input maps to multiple outputs.
True
What is the equation of a linear function?
What is the equation of the linear function corresponding to the term 'Linear function'?
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A function mapping must have unique outputs for each input, ______ or false?
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The set of points (2, 2), (3, 4), (2, 4) represents a function.
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What defines a non-linear function?
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Study Notes
Functions
- A function is a relation where each input value corresponds to exactly one output value.
- Function notation is commonly represented as f(x), indicating the output for the input x.
- Functions can be identified through mappings, tables, or graphs that exhibit this one-to-one relationship.
Non-Functions
- A relation is not a function if any input value corresponds to multiple output values.
- Examples include pairs like (1, 3) and (1, -3), where the input 1 is associated with two different outputs.
- Relations that have repeated x-values with different y-values, such as (2, 2) and (2, 4), fail the vertical line test, disqualifying them as functions.
Key Examples of Functions
- The set of ordered pairs (2, 4), (3, 4), (0, 1), (-2, 1) represents a function because each x-value is unique.
- Linear functions can be expressed in the form of an equation like y = -5x + 0.6, indicating a constant change in y with respect to x.
- Another example of a linear function is y = 4x, showcasing a straight line with a positive slope on a graph.
Key Examples of Non-Functions
- The ordered pairs (1, 3), (8, 4), (1, -3), and (9, 0) represent a non-function because the input 1 maps to two different outputs.
- In a graphical representation, a vertical line intersects the graph of a non-function at more than one point, indicating multiple outputs for a single input.
- In mapping relationships that demonstrate non-functions, such as (2, 2) and (2, 4), the x-value 2 leads to different outputs, establishing it as a non-function.
Additional Concepts
- A linear function has a constant rate of change, depicted as a straight line on a graph.
- Non-linear functions show varying rates of change and can represent curves or other complex shapes in graphs.
Summary of Definitions
- Understanding the distinction between functions and non-functions is crucial for studying algebra and advanced mathematics.
- Recognizing these relations helps in analyzing mathematical models and real-world systems effectively.
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Explore the key concepts of functions and non-functions with these flashcards. Each card provides definitions and examples to clarify these fundamental ideas in mathematics. Perfect for quick reviews and learning.
