functional dependency simply means when one attribute in a relation can be used to UNIQUELY determines another attribute. For example, assume that we have a customer entity with the following attributes:
We can state the following:
CUSTID -> LAST_NAME, FIRST_NAME, MIDDLE_INIT, ADDR1, ADDR2, CITY, STATE, ZIP, EMAIL_ADDR
That is; given a CUSTID, we can uniquely determine the other attributes. In other words, given the CUSTID we can find the LAST_NAME attribute that belongs with this CUSTID along with the other attributes. Now take the example below:
This is not valid functional dependency. The reason is that more than one customer can have the same last name but different CUSTID, FIRST_NAME, etc. For example, suppose you have "Jones" as the last name. There might be more than customer whose last name has the value "Jones". Since "Jones" cannot be used to uniquely identify a unique value for CUSTID in the relation (because which CUSTID would you be referring to?) it cannot be said that CUSTID or any of the other attributes for that matter are functionally dependent on LAST_NAME.