Unit 3: Relations and Functions Flashcards

Relations and Functions

• A relation is defined as a set of ordered pairs representing the relationship between variables.
• The independent variable, typically denoted as x, represents values chosen freely and influences the dependent variable.
• The dependent variable, usually referred to as y, takes values that rely on the output of the independent variable.
• A function is characterized by having precisely one output for each input, ensuring predictability in the relationship.
• The domain encompasses all possible input values of a function, determining what x-values can be used.
• The range includes all potential output values of a function, reflecting the resulting y-values.
• Function notation provides a clear, systematic way to express a function, detailing inputs and corresponding outputs concisely.
• A discrete function is represented graphically by isolated points, indicating distinct, non-continuous outputs.
• In contrast, a continuous function displays a graph as an unbroken line or curve, indicating no interruptions in values.

Graph Characteristics

• An x-intercept is the point where the graph crosses the x-axis, characterized by the y-coordinate being zero.
• A y-intercept is where the graph crosses the y-axis, identified by the x-coordinate being zero.
• Relative maximum points on a graph signify locations where neighboring points do not exceed the y-coordinate, indicating potential peaks.
• Relative minimum points are those where no nearby points have a lesser y-coordinate, signifying valleys in the graph.

Symmetry and Function Types

• Line symmetry refers to a situation where a line divides a figure into two halves that are mirror images, indicating symmetry in the graph.
• A linear function is defined by a graph that forms a straight line, representing a constant rate of change between variables.