f: A → B will be an into function if

The correct option is range (f) ⊂ B.

To understand why this option is correct, let us break down the definition of an into function step-by-step:

1. Definition of a Function:
A function $f:A\to B$ maps every element in the domain set $A$ to a unique element in the codomain set $B$. The set of all actual output values produced by the function is called the range of the function, which is denoted as $f\left(A\right)$ or $\text{range}\left(f\right)$.

2. Into Function vs. Onto Function:
- An onto function (or surjective function) is one where every element in the codomain $B$ has at least one pre-image in the domain $A$. In this case, the range of the function is exactly equal to the codomain, meaning $\text{range}\left(f\right)=B$.
- An into function is a function where there is at least one element in the codomain $B$ that does not have a pre-image in the domain $A$. In other words, the range of the function is a strict subset of the codomain.

3. Mathematical Representation:
For $f:A\to B$ to be an into function, the range must be properly contained within the codomain $B$ without filling it entirely. Mathematically, this is expressed as:
$\text{range}\left(f\right)\subset B$
where the symbol $\subset$ denotes a proper subset.

Therefore, the condition for $f$ to be an into function is precisely range (f) ⊂ B.