Identifying Functions Flashcards

What does the term 'input' refer to in a relation?

What does the term 'output' refer to in a relation?

Is this relation a function? (-2,-2) (2,-1) (3,0) (5,3) (5,4)

Is this relation a function? (-3,-1) (-2,0) (-1,3) (-1,0) (0,-1)

Is this relation a function? (4,11) (5,18) (6,25) (7,32) (8,39)

Is this relation a function? (10,1) (11,6) (12,11) (13,16)(14,21)

Is this relation a function? (0,1) (1,2) (2,3) (3,4) (4,4)

Function - passes the vertical line test. Is this a function?

Function - each input has exactly one output. Is this a function?

Not a function - does not pass the vertical line test. Is this a function?

Not a function - there is an input (4) that goes to two different outputs (5 and -5). Is this a function?

What is the vertical line test?

Describe a function in simple terms.

Provide an example of a function with ordered pairs.

Provide an example of a function where inputs have the same output.

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.

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.