Question

Amber, Bill, Clarence, and Diana each made a

statement abbut the relation {(1,-2), (1,2),
(3,4), (3, 4), (5,-6), (5, 6), (100, --101).
(100, 101)). Which student's statement is
completely true?
A. Amber said "It is two functions: y = (x + 1) and
y=-(x + 1) for all x in the domain."
B. Bill said "It is a function: y= + (x + 1) for all x in
the domain."
C. Clarence said "It is not a function because there
are not enough values in the domain."
D. Diana said "It is not a function because functions
must map domain values into single range
values."

Answer 1

Diana's statement is true because a function must assign exactly one output (range value) to each input (domain value) and the given relation pairs certain inputs with multiple outputs.

Step-by-step explanation:

The student's question relates to a relation given as a set of ordered pairs and requires determining which of four student statements about the relation is true. To determine if a set of ordered pairs represents a function, we apply the definition that each element of the domain must map to exactly one element of the range.

Amber's statement suggests that it is two functions, which is not applicable here as we are looking to define it as a single function or not. Bill's statement incorrectly assumes it is a function with the given formula for all domain values. Clarence's statement is incorrect because having 'enough' domain values is not a criterion for being a function.

Diana's statement is accurate because a function cannot map one domain element to more than one range element, but here, the numbers 1, 3, 5, and 100 in the domain are each paired with two different range values, violating the definition of a function.