Question

the relationship between a person’s favorite movies and their name is a ____________ relationship.
the ____________ test helps to determine if a graph represents a function by using vertical lines.
if a vertical line intersects a graph at more than one point, the graph is ____________.

Explanation:

First Question:

A person's name can be associated with multiple favorite movies (one name to many movies), so it's not a function (since a function requires each input to have only one output). So the relationship is a "non - function" or more precisely, a "one - to - many" relationship, but in terms of function terminology, it's a "non - function" or we can say "not a function" (but the blank likely expects a term related to function - non - function. Since a function has each input with one output, here one name (input) can have multiple movies (outputs), so it's a "non - function" or "not a function" but the standard term here is that it's a "relation" that is not a function, but the blank is likely for "non - function" or "not a function" or more precisely, since a function has each element in domain (name) mapping to exactly one in codomain (movie), here it's a "one - to - many" which is not a function, so the relationship is a "non - function" or "not a function". But the most appropriate term is "non - function" or "not a function". However, the first blank: A person's name (domain element) can be related to multiple favorite movies (codomain elements), so it's a "non - function" or "not a function" (or "relation" but since the question is about function - non - function, the answer is "non - function" or "not a function". But the standard answer here is "not a function" or "non - function".

The test that uses vertical lines to determine if a graph is a function is the "vertical line" test.

By the vertical line test, if a vertical line intersects a graph at more than one point, the graph does not represent a function, so the graph is "not a function" (or "not a function graph" or more precisely, "not a function" as a graph).

Answer:

not a function (or non - function)

Second Question: