Math

QuestionDetermine if each relation is a function: (a) States & Capitals, (b) States & Cities, (c) Families & Pets, (d) Families & Last names. Explain.

Studdy Solution

STEP 1

Assumptions1. A function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. . In this context, the 'Input' column represents the domain (set of inputs) and the 'Outputs' column represents the range (set of permissible outputs).

STEP 2

We need to decide whether each of the following relations is a function. A relation is a function if each input is related to exactly one output.

STEP 3

Consider the first relation States and Capitals.In this case, each state (input) has exactly one capital (output). Therefore, this relation is a function.

STEP 4

Consider the second relation States and Cities.
In this case, each state (input) can have multiple cities (outputs). Therefore, this relation is not a function.

STEP 5

Consider the third relation Families and Pets.
In this case, each family (input) can have multiple pets (outputs). Therefore, this relation is not a function.

STEP 6

Consider the fourth relation Families and Last names.
In this case, each family (input) has exactly one last name (output). Therefore, this relation is a function.

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