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]