Algebra Concepts & Connections Flashcards

Questions and Answers

What is a function?

The change in y over the change in x

The space on an axis between two points

A point on a graph

A relationship between two variables (correct)

What does the domain refer to?

All the possible values of x

What does the range refer to?

All the possible values of y

What is the x-intercept?

The point(s) where the line crosses the x-axis Signup and view all the answers

What is the y-intercept?

The point where the line crosses the y-axis Signup and view all the answers

What is the slope?

Rise over run Signup and view all the answers

What is the average rate of change?

How to measure the slope between 2 points on a curve Signup and view all the answers

What is a zero slope?

A horizontal line going left to right Signup and view all the answers

What does a positive slope indicate?

When the line goes up from left to right Signup and view all the answers

What does a negative slope indicate?

When the line goes down from left to right Signup and view all the answers

What does an undefined slope indicate?

A vertical line that goes up and down Signup and view all the answers

What is a discrete graph?

When the points on a graph are not connected Signup and view all the answers

What is a continuous graph?

When the points on a graph are connected in a line or curve Signup and view all the answers

What is an interval in graphing?

The space on an axis between two points Signup and view all the answers

Study Notes

Function and Variables

A function defines a relationship between two variables, typically represented as x and y.

Domain and Range

The domain consists of all possible x values that can be input into a function.
The range encompasses all possible y values that can result from the function.

Intercepts

The x-intercept indicates where a line intersects the x-axis, expressed as (x, 0).
The y-intercept signifies where a line meets the y-axis, expressed as (0, y).

Slope Concepts

Slope is determined by the ratio of the change in y (rise) to the change in x (run).
A zero slope indicates a horizontal line where y remains constant across values of x.
A positive slope shows that as x increases, y also increases, represented by an upward line from left to right.
A negative slope indicates that as x increases, y decreases, represented by a downward line from left to right.
An undefined slope occurs with a vertical line where x remains constant.

Rates of Change

The average rate of change measures the slope between two distinct points on a curve, highlighting the overall trend.

Graph Types

A discrete graph features individual points that are not connected, such as whole numbers or distinct time intervals.
A continuous graph has connected points that form a line or curve, representing smooth transitions without interruption.

Intervals

An interval describes the section on an axis between two specific points, utilized to identify ranges or sections within a graph.

Description

Enhance your understanding of key algebra concepts with these flashcards. Each card provides a definition of important terms such as function, domain, and intercepts. Perfect for students looking to improve their algebra skills and retain essential information.