# That seems like too little information!

Calculus Level 5

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?


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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