Algebra 1 Relations and Functions Flashcards

Questions and Answers

What is the definition of a coordinate plane?

Formed by the intersection of two number lines, the horizontal axis and the vertical axis.

What is the definition of x-axis?

The horizontal axis on a coordinate plane.

What is the definition of y-axis?

The vertical axis on a coordinate plane.

What is the definition of quadrants?

The four regions into which the x-axis and y-axis separate the coordinate plane. Signup and view all the answers

What is the definition of origin?

The point at which the x- and y-axis intersect on the coordinate plane (0,0). Signup and view all the answers

What is the definition of an ordered pair?

A set of numbers, or coordinates, written in the form (x, y). Signup and view all the answers

What is the definition of a x-coordinate?

The x-value of an ordered pair, represents the horizontal placement of the point. Signup and view all the answers

What is the definition of a y-coordinate?

The y-value of an ordered pair, represents the vertical placement of the point. Signup and view all the answers

What is the definition of a discrete graph?

A graph that consists of points that are not connected. Signup and view all the answers

What is the definition of a continuous graph?

A function graphed with a line or smooth curve. Signup and view all the answers

What is the definition of a relation?

A set of ordered pairs. Signup and view all the answers

What is the definition of domain?

The set of first numbers (x-values) of the ordered pairs of a relation. Signup and view all the answers

What is the definition of range?

The set of second numbers (y-values) of the ordered pairs of a relation. Signup and view all the answers

What is the definition of mapping?

Illustrates how each element of the domain is paired with an element of the range. Signup and view all the answers

What is the definition of function?

A relation in which each element of the domain is paired with exactly one element of the range. Signup and view all the answers

What is the definition of function notation?

A way to name a function that is defined by an equation. Signup and view all the answers

What is the definition of input?

A value substituted for the 'x'-value in a function. Signup and view all the answers

What is the definition of output?

The result of substituting a value into a function. Signup and view all the answers

What is the definition of a vertical line test?

If any vertical line passes through the graph of a relation no more than once, than it is a function. Signup and view all the answers

What is the definition of zeros?

The x-intercepts of the graph of a function. The points for which f(x)=0. Signup and view all the answers

Study Notes

Coordinate Plane

Formed by the intersection of horizontal (x-axis) and vertical (y-axis) number lines.

Axes

x-axis: The horizontal axis on a coordinate plane.
y-axis: The vertical axis on a coordinate plane.

Quadrants

The coordinate plane is divided into four regions, called quadrants, by the x-axis and y-axis.

Origin

The intersection point of the x-axis and y-axis, designated as (0,0).

Coordinates

Ordered pair: A set of numbers written in the form (x,y).
x-coordinate: The first number in an ordered pair, indicating horizontal placement.
y-coordinate: The second number in an ordered pair, indicating vertical placement.

Graph Types

Discrete graph: Consists of unconnected points.
Continuous graph: Represented by a line or smooth curve.

Relations and Functions

Relation: A collection of ordered pairs.
Domain: The set of all first elements (x-values) in a relation.
Range: The set of all second elements (y-values) in a relation.
Mapping: Illustrates the pairing between elements of domain and range.
Function: A special relation where each domain element corresponds to exactly one range element.

Function Notation

A systematic way to name a function defined by an equation.

Inputs and Outputs

Input: The value substituted for the x-value in a function.
Output: The result obtained after substituting an input value into a function.

Vertical Line Test

A method to determine if a relation is a function; if a vertical line intersects the graph at most once, it is classified as a function.

Zeros

Also known as x-intercepts, these points occur where the function's output (f(x)) equals zero.

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Description

This quiz features flashcards focused on key definitions related to the coordinate plane, including terms like x-axis and y-axis. It's designed to help students grasp essential concepts in Algebra 1. Test your understanding and improve your vocabulary in this foundational mathematical topic.