At a local pizzeria, a pizza with one topping is 9.99. You can add additional toppings for 1.25 each. The pizzeria's menu lists 10 different toppings. Write a function C(x) that represents the cost of a pizza with at least one topping, where x is the number of toppings. Find the domain and range.

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brainygeek2002 brainygeek2002

17-09-2022
Mathematics

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At a local pizzeria, a pizza with one topping is 9.99. You can add additional toppings for 1.25 each. The pizzeria's menu lists 10 different toppings. Write a function C(x) that represents the cost of a pizza with at least one topping, where x is the number of toppings. Find the domain and range.

Answer :

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MrRoyal MrRoyal · Answer 1 · 2022-09-20T15:42:07-04:00

The function C(x) that represents the cost of a pizza with at least one topping, where x is the number of toppings is C(x) = 9.99 + 1.25x

The domain is x >= 0 and the range is c(x) >= 9.99

Write a function C(x) that represents the cost of a pizza with at least one topping, where x is the number of toppings.

The given parameters are:

One topping = 9.99

Additional topping = 1.25 each

We have x to represent the number of toppings

This means that

C(x) = One topping + Additional topping * x

So, we have

C(x) = 9.99 + 1.25x

How to find the domain and range?

We have

C(x) = 9.99 + 1.25x

The smallest number of topping is 0

So, the domain is x >= 0

Substitute 0 for x in C(x) = 9.99 + 1.25x

C(0) = 9.99 + 1.25(0)

This gives

C(0) = 9.99

So, the range is c(x) >= 9.99

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eashansarraf eashansarraf · Answer 2 · 2022-09-21T22:49:32-04:00

Answer:
C(x) = 8.74 + 1.25x

Domain: 1 ≤ x ≤ 10

Range: [9.99, 21.24]

Step-by-step explanation:

a) We need to find the function C(x) that represents the cost of a pizza with at least one topping, where x is the number of toppings.

We know that a pizza with one topping is $9.99 and that you can add additional toppings for 1.25 each.

So the equation is C(x) = 9.99 + 1.25x right?

Not really... Since $9.99 is the price of a pizza and 1 topping, we need to subtract 1 from x otherwise we would be paying for a pizza with 2 toppings when we had ordered a pizza with 1!

So the new equation is:

C(x) = 9.99 +1.25(x - 1)

or, C(x) = 9.99 + 1.25x - 1.25

or, C(x) = 1.25x + 8.74

b) We need to find the Domain of C(x).

We know that the pizzeria's menu lists 10 different toppings and that a pizza has at least one topping.

So we can choose up to 10 different toppings. And we need at least 1 topping.

∴ Domain is 1 ≤ x ≤ 10.

b) We need to find the Range of C(x).

We know that the domain of C(x) is 1 ≤ x ≤ 10, and that a pizza with 1 topping is $9.99.

Since we already know the minimum (9.99) all we have to do is find the maximum. We can do that by plugging in 10 into C(x) since it is the maximum of our domain.

C(10) = 1.25(10) + 8.74

or, C(10) = 12.50 + 8.74

or, C(10) = 21.24

∴ Range of C(x) = [9.99, 21.24]

Answer:

C(x) = 8.74 + 1.25x

Domain: 1 ≤ x ≤ 10

Range: [9.99, 21.24]