Questions and Answers
What is a relation?
A relation is a set of ordered pairs.
What is the domain of a relation?
The domain of a relation is the set of all first components of the ordered pairs.
Can a relation in which a second component corresponds to more than one first component be a function?
False
Explain why the vertical line test works.
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Do all linear equations in two variables define functions?
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What is the connection between function notation to evaluate a function at certain values and ordered pair solutions of the function?
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How do you find the domain of a function given its graph?
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Study Notes
Relations and Functions
- A relation consists of a set of ordered pairs, where each pair is made up of a first component (input) and a second component (output).
- The domain of a relation includes all the first components from the ordered pairs, representing possible input values.
Functions
- A relation can have a second component that corresponds to multiple first components, but it will not be a function unless each first component only maps to one second component.
- The vertical line test is a method used to determine if a graph represents a function; if any vertical line crosses the graph at more than one point, it indicates that there is an x-value mapping to multiple y-values, thus not a function.
Linear Equations
- Not every linear equation in two variables defines a function; specifically, equations of the form x = c represent vertical lines and do not meet the criteria for functions.
Function Notation
- Function notation shows the input value for x and the resulting f(x) corresponds to an ordered pair (x, y) that represents a solution of the function.
Finding Domain from Graphs
- To determine the domain of a function using its graph, identify the set of x-values where the graph exists or is defined.
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Test your understanding of intermediate algebra concepts with these flashcards. Each card defines key terms related to relations and functions. Perfect for quick revision or self-assessment before exams.