Question

At the fair you buy an unlimited ride pass for $22 and plan to play some games costing $2.50 per game. Write a function in x that represents the total amount you spend on rides and games at the fair. Be sure to indicate any domain restrictions.The option box of the greater than or less than is interchangable. Thanks for the help!

Answer 1

The function f(x) = 2.50x + 22 models the total spending at the fair, accounting for a $22 unlimited ride pass and $2.50 per game. The domain is restricted to non-negative integers.

The function f(x) = 2.50x + 22 represents the total amount spent at the fair, considering an unlimited ride pass for $22 and playing games costing $2.50 each. In this function, x represents the number of games played, and f(x) gives the total cost incurred.

The term 2.50x accounts for the cost of playing games, where $2.50 is the cost per game, and x is the number of games played. The constant term 22 represents the cost of the unlimited ride pass, which is a fixed expense regardless of the number of games played.

It's important to note that the domain of this function is restricted to non-negative integers since the number of games played cannot be negative or in fractions. Thus, x must be an element of the set of non-negative integers (x in {0, 1, 2, 3, ...}). In the context of this problem, it wouldn't make sense to play a negative or fractional number of games.

Answer 2

f(x) = 2.50x + 22

Step-by-step explanation

Each game costs $2.50, so the cost for x games is 2.50x. To this, we have to add the initial cost of the unlimited ride pass, $22. The function is f(x) = 2.50x + 22.

The domain of this function is given by what x represents. In this case, x represents the number of games you play at the fair so it cannot be negative - note that you can't play -5 games. Hence, the domain is x ≥ 0, if x is an integer