Mr. Borden was given a $50 gift card to use at the bowling alley. It costs him $10 per night to bowl. Each time he goes to the bowling alley he records the amount he has used and the amount he has left. If x is the number of nights bowled, b(x) is the balance on the gift card. Discreet

For each night that he goes to play, $10 are discounted from the card, then if he went x nights to play, the amount of money that there is in the card is:

b(x) = $50 - $10*x

Now, notice that x must be a whole number because this measures the number of nights that he went to play, and we can not have rational numbers to describe this.

Then the domain of this function will be discrete (and this implies that the range must also be discrete)

Where the possible values of x are:

{0, 1, 2, 3, 4, 5}

(after x = 5, there is no more money in the card)

And the possible values of b(x) are:

{$0, $10, $20, $30, $40, $50}