Question

A local ice rink is hosting a skating competition that will determine whether or not skaters qualify to compete regionally. The registration for this event is limited to 50
entrants. The registration fee is $150. Consider a function that represents the total registration fees the rink can collect for this event.


Describe the domain of the function.


Please help !

Answer 1

Answer:

Function: $f(x) =\left \ {{150x;\ 0\le x\ \le 50} } \right.$

Domain: $0 \le x\ \le 50$

Step-by-step explanation:

Given

Registration Fee = 150

Entrants = 50 (maximum)

Solving (a): Create a function

Let the number of entrants be x.

If 1 entrant pays 150, then x entrants will pay 150x.

So:

$f(x) = 150x$

The minimum entrant is 0 (i.e. no entrant shows up) and from the question, the maximum is 50

So, the domain can be represented as: $0 \le x\ \le 50$

Hence, the function is:  $f(x) =\left \ {{150x;\ 0\le x\ \le 50} } \right.$

(b) : The domain

The domain has been described above as:

"The minimum entrant is 0 (i.e. no entrant shows up) and from the question, the maximum is 50"

"So, the domain can be represented as: $0 \le x\ \le 50$"