Math 3.2 Intermediate Algebra Flashcards
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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.

<p>If a vertical line intersects a graph two (or more) times, then there's an x-value corresponding to two (or more) different y-values, thus the relation is not a function.</p> Signup and view all the answers

Do all linear equations in two variables define functions?

<p>False</p> Signup and view all the answers

What is the connection between function notation to evaluate a function at certain values and ordered pair solutions of the function?

<p>Using function notation, the replacement value for x and the resulting f(x) or y-value corresponds to an ordered pair (x,y) solution to the function.</p> Signup and view all the answers

How do you find the domain of a function given its graph?

<p>To find the domain of a function from its graph, determine the set of x-values for which the graph is defined.</p> Signup and view all the answers

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.

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