De las siguientes relaciones entre dos variables, razona cuáles son funcionales y cuáles no: a. Edad – altura de la persona a lo largo de su vida b. Altura – edad de la persona c. Precio de la gasolina – día del mes d. Día del mes – precio de la gasolina e. Un número y su quinta parte f. Un número y su cuadrado g. Un número y su raíz cuadrada

In this problem, we need to describe the relation between variables, if that relation is functional or not. It's important to say that we assumed that the first variable is independent, and the second is dependent.

Age - Height of the person along his life: These variable are functinal and make total sense, because through time the person grows, which means the height changes as the age increases. These variables have a proportional relationship.

Height - Age of the person: These relation is not functional, becasuse age can't be a dependent variable, beacuse the age of a person doesn't depends on his height.

Gasoline price - Day of the Month: These relation is not functional, becasue time must be the independent variable.

Day of the Month - Gasoline price: These realation make sense, beacuse the price of the gasoline can be depedent of the day of the month.

A number and its fifth part: Notice that the fifth part depends on the number, it's defined by it, so this can be a function.

A number and its square root: These two variables represent a function, where "a number" represents the domain value and "its square root" represents a range vale.

a negative exponent is translated as follows:

so, we have