The type of nucleic acid that passes from parent to offspring and directs all the cells functions is deoxyribonucleic acid (DNA).

Here's why:

* Inheritance: DNA is the molecule that carries the genetic instructions from parents to offspring. It's found in the chromosomes within the nucleus of each cell.

* Directs cell functions: DNA contains the code for building and maintaining an organism. This code is used to create proteins, which perform a vast array of functions in the cell, from structural support to enzymatic activity.

* RNA's role: While RNA (ribonucleic acid) is also important in protein synthesis and other cellular functions, it doesn't carry the primary genetic information that is passed down. It acts as a messenger and worker molecule, carrying instructions from DNA and helping to build proteins.