Questions and Answers
What is a relation?
What is an independent variable?
the variable in a relation, usually x, with a value that is subject to choice
What is a dependent variable?
the variable in a relation, usually y, with values that depend on x
In a function, there can be multiple outputs for every input.
Signup and view all the answers
What is the domain of a function?
Signup and view all the answers
What is the range of a function?
Signup and view all the answers
What is function notation?
Signup and view all the answers
A discrete function has a graph that is an unbroken line.
Signup and view all the answers
A continuous function has gaps or breaks in its graph.
Signup and view all the answers
What is an x-intercept?
Signup and view all the answers
What is a y-intercept?
Signup and view all the answers
What is a relative maximum?
Signup and view all the answers
What is a relative minimum?
Signup and view all the answers
What is line symmetry?
Signup and view all the answers
What defines a linear function?
Signup and view all the answers
Study Notes
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.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
Explore essential terms and definitions related to relations and functions in mathematics with these flashcards. Understand key concepts like independent and dependent variables, as well as the definition of a function.
