Answer: Hello there!
A function is a mathematical construction, where you put a number, the input, and the function gives another number, the output.
A function is defined with this rule:
an input number can't have more than one output number associated.
The ordered pairs of age and height, where the age is the input, can represent a function, because if you only measure once a year, for every age there is only one height associated. Then these pairs represent a function.
If you took the other way, where the input is the height and the output is the age, this pairs does not necessarily represent a function, because at two different ages you could have the same height, this means that one value of height has more than one age associated, and this does not represent a function.