Questions and Answers
What is a function?
A relation in which for every input there is exactly one output (for every x there is just one y).
What does the term 'input' refer to in a relation?
The first coordinate of an ordered pair in a relation (x,y); also called the domain.
What does the term 'output' refer to in a relation?
The second coordinate of an ordered pair in a relation (x,y); also called the range.
Is this relation a function? (-2,-2) (2,-1) (3,0) (5,3) (5,4)
Signup and view all the answers
Is this relation a function? (-3,-1) (-2,0) (-1,3) (-1,0) (0,-1)
Signup and view all the answers
Is this relation a function? (4,11) (5,18) (6,25) (7,32) (8,39)
Signup and view all the answers
Is this relation a function? (10,1) (11,6) (12,11) (13,16)(14,21)
Signup and view all the answers
Is this relation a function? (0,1) (1,2) (2,3) (3,4) (4,4)
Signup and view all the answers
Function - passes the vertical line test. Is this a function?
Signup and view all the answers
Function - each input has exactly one output. Is this a function?
Signup and view all the answers
Not a function - does not pass the vertical line test. Is this a function?
Signup and view all the answers
Not a function - there is an input (4) that goes to two different outputs (5 and -5). Is this a function?
Signup and view all the answers
What is the vertical line test?
Signup and view all the answers
Describe a function in simple terms.
Signup and view all the answers
Provide an example of a function with ordered pairs.
Signup and view all the answers
Provide an example of a function where inputs have the same output.
Signup and view all the answers
Study Notes
Function Definition
- A function is a relation where each input (x) corresponds to exactly one output (y).
- Functions can be identified through ordered pairs, denoted as (x, y).
Key Terms
- Input: The first coordinate in an ordered pair; also known as the domain.
- Output: The second coordinate in an ordered pair; also known as the range.
Identifying Functions
- A relation is not a function if an input corresponds to multiple outputs. This is evident in examples with repeated first coordinates resulting in different second coordinates.
- Examples of relations that are not functions:
- (-2,-2), (2,-1), (3,0), (5,3), (5,4) fails because (5,3) and (5,4) have the same input.
- (-3,-1), (-2,0), (-1,3), (-1,0), (0,-1) fails because (-1,3) and (-1,0) have the same input.
Examples of Functions
- A relation is a function when every input has one unique output:
- (4,11), (5,18), (6,25), (7,32), (8,39) is a function due to unique outputs for each input.
- (0,1), (1,2), (2,3), (3,4), (4,4) meets the function criteria.
Vertical Line Test
- A graph represents a function if a vertical line intersects the graph at no more than one point.
- If a vertical line crosses at multiple points, the relation is classified as not a function.
Summary of Function Characteristics
- Functions consistently maintain one output for each input.
- Any instance of a shared input leading to multiple outputs rules out the possibility of a function designation.
Additional Notes
- Relations may still be called functions if mixed outputs occur only under distinct inputs.
- Examples of relations might vary but should adhere to the fundamental rules of input-output pairing to be considered functions.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
Test your understanding of functions with these flashcards. Each card provides key terms and definitions, helping you discern input and output in relations. Perfect for students learning about functions in mathematics.
