For deducing the answers, you can use what does function of something means.
a) Yes, height of the stack is a function of the number of cups in the stack.
b) Yes, we can say that the number of cups in a stack is a function of the height of the stack.
There are two sets of values. When we connect first set's values with other set, it is called mapping one set's value to other set. All type of mappings are called relations.
Such relations which are such that each element of the first set(also called input set or domain) is mapped to only one value of the other set(called codomain, and if all values are occupied, then called range or output set), then such relation is called function.
So, for a mapping to be function, we need each input to be mapped to only one output.
First, know that as the amount of cup is increasing, the height of the stack is increasing. This shows that the number of cups in the stack of the cups is related to the height of the stack.
Now we have to check if this can be a function.
For height of stack to be a function of the number of cups in the stack, we need input set(which is number of cups) to map to single value to output set(the height of the stack).
Since a fixed amount of cups in the stack cannot have two different height, thus there is single output to each of the input.
Thus,
[tex]h = f(n)[/tex]
(where f is the function of n which is number of cups and it shows that h is function of n where h denotes the height of the stack)
Similar to the above condition, we now have input as height of the stack and output as the number of cups.
Since one height of the stack cannot have different amount of cup(assuming that the arrangement was uniform. This assumption is very important in deciding if that relation will be a function or not. Since it was given that the cups are identical, we can assume that the stack was formed uniformly unless otherwise stated), thus we have one height mapping to one value of n, thus
[tex]n = g(h)[/tex] where g is a function of h
Thus,
a) Yes, height of the stack is a function of the number of cups in the stack.
b) Yes, we can say that the number of cups in a stack is a function of the height of the stack.
Learn more about functions here:
https://brainly.com/question/13395697
