The problem is asking for the conditions that define the left-hand limit of a function $f(x)$ as $x$ approaches $a$.

The correct way to fill in the blanks is:

"We say $\lim_{{x \to a^-}} f(x) = L$ if $f(x)$ approaches $L$ as $x$ approaches $a$ with $x < a$."

Thus, the answers are:

1. $f(x)$ approaches $L$
2. $x$ approaches $a$
3. $x < a$

Would you like more details on the concept of one-sided limits or any further clarification? Here are five related questions:

1. What is the right-hand limit, and how is it defined?
2. How do you determine if a two-sided limit exists?
3. What are some examples of functions with undefined limits at certain points?
4. Can a function have different left-hand and right-hand limits at the same point?
5. What is the relationship between limits and continuity?

Tip: One-sided limits are often used to understand behavior at points of discontinuity or in piecewise functions!