Question

Sarah has sold $33 worth of tickets to the comedy show. She has 4 tickets left to sell for $11 per ticket?

What is the function notation?
What is the domain and range?
Is this problem continuous or discrete?​

Answer 1

Part A)
`f(x)=11x+33`

Part B) The domain is the interval [0,1,2,3,4] and the range is the interval [$33,$44,$66,$77]

Part C) This problem is a discrete function

Explanation:

Part A) What is the function notation?

Let

x -----> the number of tickets left to sell

f(x) -----> amount of money for ticket sales

we know that

The amount of money for ticket sales is equal to the cost of each ticket by the number of tickets left to sell plus the amount of money from tickets already sold.

so

The function notation is

`f(x)=11x+33`

Part B) What is the domain and range?

A reasonable domain is the number of tickets left to sell

so

[0,1,2,3,4] -----> The domain is a set of input values consisting of only certain numbers in an interval

Find the range

For x=0 ----->
`f(0)=11(0)+33=\$33`

For x=1 ----->
`f(1)=11(1)+33=\$44`

For x=3 ----->
`f(3)=11(3)+33=\$66`

For x=4 ----->
`f(4)=11(4)+33=\$77`

so

The range is the interval -----> [$33,$44,$66,$77]

Part C) Is this problem continuous or discrete?​

we know that

A discrete function allows the x-values to be only certain points in the interval, usually only integers or whole numbers, and the continuous function allows the x-values to be ANY points in the interval, including fractions, decimals, and irrational values.

In this problem

the x-values are only certain points in the interval

therefore

Is a discrete function