Let $f : \mathbb{C} \to \mathbb{C}$ be holomorphic on $\mathbb{C}$.

Also, suppose the following holds: $\big|f(z)\big| \to +\infty \text{ as } |z| \to +\infty.$

Then which of the following **necessarily** holds?

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**Details and Assumptions:**

- $\text{Image}(f)$ denotes the range of $f.$
- $A \setminus B = \{x \in A: \, x \notin B\}.$
- If more than one statement is necessarily true,
**choose the strongest**.

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