Answer
Not a function.
Work Step by Step
A function is a correspondence between a first set, called the domain,
and a second set, called the range,
such that EACH member of the domain corresponds to EXACTLY ONE member of the range.
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Keywords are emphasized.
We see from the graphical definition of the correspondence that
"Julia Roberts" from the domain has more than one corresponding value in the range (she has three).
So, the "exactly one" clause has been violated.
Not a function.
Note: The same clause is violated for "Denzel Washington" from the domain.