Algebra 1 EOC Review Flashcards

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.

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.