Question

george moved to a new house. he tracked his electricity consumption over a period of 14 months. consider the graph below which shows the relationship between his monthly electricity consumption, y, and x, which represents the number of months since he started tracking.
which of the following describes the graph?
a. both a relation and a function
b. neither a function nor a relation
c. a relation only
d. a function only

Explanation:

1. Definition of a Relation: A relation is any set of ordered pairs \((x, y)\). The graph shows ordered pairs \((x, y)\) where \(x\) is the number of months and \(y\) is electricity consumption, so it is a relation.
2. Definition of a Function: A function is a relation where each input \(x\) has exactly one output \(y\). For the graph, each \(x\) (month) maps to only one \(y\) (consumption) (passes the vertical line test). Thus, it is also a function.

Since it satisfies both, the graph is both a relation and a function.

Answer:

A. both a relation and a function