Algebra 1 EOC Review Flashcards

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Questions and Answers

What is a relation?

set of unpaired values

set of ordered pairs (correct)

set of random numbers

set of linear equations

What are the x and y coordinates of a point on the coordinate plane called?

ordered pair

What is the coordinate plane?

a plane formed by 2 perpendicular lines called axes

A function is a special relation where each x-value is paired with more than one y-value.

False Signup and view all the answers

What is the domain in a function?

set of all of the possible x-values Signup and view all the answers

What is the range in a function?

set of all the possible y-values Signup and view all the answers

Define a variable.

a letter or symbol that stands for a number Signup and view all the answers

What is an independent variable?

the input or cause in a situation Signup and view all the answers

What is a dependent variable?

the output or result in a situation Signup and view all the answers

What are other names for 'x'?

input Signup and view all the answers

What are other names for 'y'?

output Signup and view all the answers

A relation passes the vertical line test if a vertical line touches it only once.

True Signup and view all the answers

Define a discreet function.

data appears as individual points on a graph Signup and view all the answers

Define a continuous function.

data appears as a smooth curve on a graph Signup and view all the answers

What does 'm' represent in the equation y = mx + b?

slope Signup and view all the answers

What does 'b' represent in the equation y = mx + b?

the y-intercept Signup and view all the answers

How does changing 'm' in the slope-intercept form affect the line?

changes the steepness of the line Signup and view all the answers

How does changing 'b' in the slope-intercept form affect the line?

moves the line up or down the y-axis Signup and view all the answers

What is the linear parent function?

y = x Signup and view all the answers

Define slope.

the steepness of a line, vertical change/horizontal change Signup and view all the answers

Why is slope important for linear equations and lines?

linear equations have constant slopes Signup and view all the answers

What slope does a horizontal line have?

slope = 0 Signup and view all the answers

What slope does a vertical line have?

undefined slope Signup and view all the answers

What is the x-intercept?

the point where the graph crosses the x-axis Signup and view all the answers

What is the y-intercept?

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

What is Direct Variation?

y = mx or y = ax or y = kx Signup and view all the answers

What is Inverse Variation?

y = 1/x Signup and view all the answers

What is a linear inequality?

an equation with <, >, ≤, or ≥ instead of = Signup and view all the answers

How do the slopes of parallel lines compare?

they are the same Signup and view all the answers

How do the slopes of perpendicular lines compare?

they are opposite and fraction is flipped Signup and view all the answers

What is a line of best fit?

a line drawn through points on a scatterplot to estimate the best line through the data Signup and view all the answers

What is a system of equations?

2 or more equations graphed on the same coordinate plane Signup and view all the answers

Study Notes

Relations and Functions

A relation is a set of ordered pairs, defining a relationship between two variables.
An ordered pair consists of x and y coordinates representing a specific point on the coordinate plane.
The coordinate plane is formed by two perpendicular lines known as axes (x-axis and y-axis).
A function is a relation where each x-value corresponds to a single y-value, passing the vertical line test.

Domain and Range

The domain encompasses all possible x-values (inputs) in a function.
The range includes all possible y-values (outputs) that correspond to the domain.

Variables in Functions

A variable is a symbol (typically a letter) representing a number that can vary.
The independent variable (x) is the input or cause in a function that can be controlled.
The dependent variable (y) is the output or result that cannot be controlled, represented on one side of the equation.

Identifying Variables

Other names for x include: domain, independent variable, and input.
Other names for y include: range, dependent variable, and output.

Graphical Tests and Types of Functions

The vertical line test determines if a relation is a function; a vertical line must touch the graph at only one point.
Discrete functions display data as distinct points that can't be further divided (e.g., people).
Continuous functions reveal data as a smooth curve, representing information that can be divided into smaller pieces (e.g., time).

Graphing Functions

The graph of a linear function features a straight line, characterized by a constant slope.
The graph of a quadratic function is a parabola opening upwards or downwards.
The graph of an inverse function reflects that a variable decreases as another increases.
Exponential decay graphs decrease rapidly initially and then level off.
Exponential growth graphs increase rapidly, showing upward trends.

Slope-Intercept Form

In the equation y = mx + b:
- "m" represents the slope, indicating the steepness of the line.
- "b" represents the y-intercept, the point where the line crosses the y-axis.

Slope Characteristics

Adjusting "m" modifies the steepness of the line, while changing "b" moves the line vertically on the graph.
The linear parent function is expressed as y = x.

Understanding Slope

Slope is defined as the vertical change divided by horizontal change.
For linear equations, slope remains constant throughout the line.
A horizontal line has a slope of 0, while a vertical line has an undefined slope.

Intercepts

The x-intercept is where the graph crosses the x-axis, represented as (x, 0).
The y-intercept is where the graph crosses the y-axis, represented as (0, y).

Variations

Direct Variation follows the equation y = mx, with a y-intercept at (0, 0).
Inverse Variation is represented by y = 1/x, where as one variable increases, the other decreases.

Inequalities and Lines

A linear inequality includes symbols like <, >, ≤, or ≥ in place of an equals sign.
Parallel lines share the same slope, while perpendicular lines have slopes that are opposite and reciprocal (flipped fraction).

Additional Concepts

A line of best fit is drawn on a scatterplot to represent the trend of the data.
A system of equations comprises two or more equations plotted on the same coordinate plane.

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Description

Prepare for the Algebra 1 End-of-Course exam with these flashcards. Each card covers key concepts such as relations, ordered pairs, and functions. Perfect for quick review and study before the test.