Contains information that determines a cell's purpose and function.

cytoplasm
dna
the nucleus
an organelle

DNA is the correct answer.

Step-by-step explanation:

" Deoxyribonucleic acid (DNA) , a self-replicating material which is present in nearly all living organisms as the main constituent of chromosomes. It is the carrier of genetic information "

                               OR

" Deoxyribonucleic acid ( DNA) is a molecule composed of two chains that coil around each other to form a double helix carrying the genetic instructions used in the growth, development, functioning, and reproduction of all known living organisms and many viruses "

Hence, the correct answer among all the options  is DNA .

i.e.

DNA contains information that determines a cell's purpose and function.

Integers may be positive or negative. They are whole numbers. 
Rational expression is a fraction wherein a numerator and/or a denominator are polynomials.

Division of integers is like dividing whole numbers. You only have to take not of the positive or negative sign of each integer to determine the sign of the quotient.

Division of rational expression:
1) flip and multiply
2) factor the numerator and denominator
3) cancel duplicate factors and simplify.