Podcast
Play an AI-generated podcast conversation about this lesson
Download our mobile app to listen on the go
Get App
Questions and Answers
What is the term for a relation where each input has exactly one output?
What is the term for a relation where each input has exactly one output?
- Function (correct)
- Neither A nor B
- Both A and B
- Not a Function
What term describes a relation where at least one input has more than one output?
What term describes a relation where at least one input has more than one output?
- Function
- Not a Function (correct)
- Both A and B
- Neither A nor B
What is a function?
What is a function?
A relation where each input has exactly one output.
What does it mean when a relation is described as not a function?
What does it mean when a relation is described as not a function?
Signup and view all the answers
Flashcards are hidden until you start studying
Study Notes
Understanding Functions and Non-Functions in Graphs
- A function is a relationship where each input has exactly one output.
- In a function graph, any vertical line drawn will intersect the graph at most once, representing a single y-value for each x-value.
- Not a function indicates a relationship where at least one input has multiple outputs, violating the strict definition of a function.
Characteristics of Functions
- Functions can be represented as equations, graphs, or tables.
- Example forms of functions include linear, quadratic, polynomial, and exponential.
- Functions may have domains and ranges that influence their behavior and characteristics.
Identifying Non-Functions
- A graph shows as not a function if it fails the vertical line test, meaning a vertical line intersects the graph at two or more points.
- Common examples of non-functions include circles and parabolas opening sideways.
- Non-functions can also be described through multi-valued relationships, such as square roots or absolute values that produce multiple outputs for a single input.
Types of Functions
- Linear Functions: Represented by a straight line; has a constant slope.
- Quadratic Functions: Form a parabola and can open upwards or downwards.
- Exponential Functions: Grow rapidly and are characterized by their base raised to a variable exponent.
Examples
- A relation defined as y = 2x + 3 is a function.
- A relation like x² + y² = r² represents a circle and is not a function.
Conclusion
- Understanding the distinction between functions and non-functions is critical for working with graphs in mathematics, impacting problem-solving and analysis techniques used across various mathematical concepts.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
