Question

Use the mapping to

a. determine whether the relation is a function

b. find the domain of the relation

c. find the range of the relation.

Short answer

(a)The relation is not a function.

(b) Domain is: {NCB, HGTV, HBO}

(c) Range is: {Ellen Degeneres Show, Law and order, Tonight Show, Property Brothers, House Hunters, Love It or List It, Game of Thrones, True Detective, Sesame Street}

Step-by-step solution

Part(a) Step 1: Definition

A function is a relation that assigns to each element in its domain exactly one element in the range. For each ordered pair in the relation, each x-value is matched with only one y-value.

Part(a) Step2: Explanation

All networks NBC, HGTV and HBO have three programs.

So, each x-value is not matched with only one y-value.

So this relation is not a function.

Part(b) Step 1: Find domain

The domain is the set of all x-values in the relation.

The domain is:

{NCB, HGTV, HBO}

Part(c) Step 1: Find range

The range is the set of all y-values in the relation.

The range is:

{Ellen Degeneres Show, Law and order, Tonight Show, Property Brothers, House Hunters, Love It or List It, Game of Thrones, True Detective, Sesame Street}