Math 3.2 Intermediate Algebra Flashcards

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.

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. Signup and view all the answers

Do all linear equations in two variables define functions?

False 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?

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. Signup and view all the answers

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

To find the domain of a function from its graph, determine the set of x-values for which the graph is defined. 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.

Description

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.